메뉴 건너뛰기




Volumn 1-3, Issue , 2006, Pages 125-291

Differential Equations with Hysteresis via a Canonical Example

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84884740135     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-012480874-4/50005-1     Document Type: Chapter
Times cited : (32)

References (198)
  • 3
    • 84884783638 scopus 로고
    • Transaction of the Royal Society of London 176, Oxford and New York II
    • Ewing J.A. Experimental research in magnetism 1895, Transaction of the Royal Society of London 176, Oxford and New York II.
    • (1895) Experimental research in magnetism
    • Ewing, J.A.1
  • 5
    • 84884809692 scopus 로고    scopus 로고
    • Strong solutions to equations of visco-thermo-plasticity with a temperature-dependent hysteretic strain-stress law
    • Paris, 1997, Kluwer Acad. Publ., Dordrecht, Variations of Domain and Free-boundary Problems in Solid Mechanics
    • Krejcí P., Sprekels J. Strong solutions to equations of visco-thermo-plasticity with a temperature-dependent hysteretic strain-stress law. Solid Mech. Appl . 1999, vol. 66:237-244. Paris, 1997, Kluwer Acad. Publ., Dordrecht.
    • (1999) Solid Mech. Appl . , vol.66 , pp. 237-244
    • Krejcí, P.1    Sprekels, J.2
  • 7
    • 0003828740 scopus 로고    scopus 로고
    • Hysteresis and Phase Transitions
    • Springer-Verlag, New York
    • Brokate M., Sprekels J. Hysteresis and Phase Transitions. Applied Mathematical Sciences 1996, vol. 121. Springer-Verlag, New York.
    • (1996) Applied Mathematical Sciences , vol.121
    • Brokate, M.1    Sprekels, J.2
  • 9
    • 0037309096 scopus 로고    scopus 로고
    • Homogenization of two-phase flows in porous media with hysteresis in the capillary relation
    • Beliaev A. Homogenization of two-phase flows in porous media with hysteresis in the capillary relation. European J. Appl. Math. 2003, 14(1):61-84.
    • (2003) European J. Appl. Math. , vol.14 , Issue.1 , pp. 61-84
    • Beliaev, A.1
  • 10
    • 0039248890 scopus 로고    scopus 로고
    • A note on hysteresis in glaciology
    • Díaz J.I., Schiavi E. A note on hysteresis in glaciology. Appl. Math. Lett. 2000, 13(3):125-129.
    • (2000) Appl. Math. Lett. , vol.13 , Issue.3 , pp. 125-129
    • Díaz, J.I.1    Schiavi, E.2
  • 11
    • 0025399031 scopus 로고
    • Thermo-mechanical evolution of shape memory alloys
    • Colli P., Frémond M., Visintin A. Thermo-mechanical evolution of shape memory alloys. Quart. Appl. Math. 1990, 48(1):31-47.
    • (1990) Quart. Appl. Math. , vol.48 , Issue.1 , pp. 31-47
    • Colli, P.1    Frémond, M.2    Visintin, A.3
  • 12
    • 23244432652 scopus 로고    scopus 로고
    • Model Department, SIAM, Philadelphia
    • Smith R. Smart Material Systems 2005, Model Department, SIAM, Philadelphia.
    • (2005) Smart Material Systems
    • Smith, R.1
  • 14
    • 0004259442 scopus 로고
    • Differential Models of Hysteresis
    • Springer-Verlag, Berlin
    • Visintin A. Differential Models of Hysteresis. Applied Mathematical Sciences 1994, vol. 111. Springer-Verlag, Berlin.
    • (1994) Applied Mathematical Sciences , vol.111
    • Visintin, A.1
  • 15
    • 0004267747 scopus 로고
    • (Translated from the Russian by Marek Niezgódka), Springer-Verlag, Berlin
    • Krasnosel'skii M.A., Pokrovskii A. Systems with Hysteresis 1989, (Translated from the Russian by Marek Niezgódka), Springer-Verlag, Berlin.
    • (1989) Systems with Hysteresis
    • Krasnosel'skii, M.A.1    Pokrovskii, A.2
  • 16
  • 19
    • 3042884683 scopus 로고
    • Semilinear parabolic equations with Preisach hysteresis
    • Little T.D., Showalter R.E. Semilinear parabolic equations with Preisach hysteresis. Differential Integral Equations 1994, 7(3-4):1021-1040.
    • (1994) Differential Integral Equations , vol.7 , Issue.3-4 , pp. 1021-1040
    • Little, T.D.1    Showalter, R.E.2
  • 20
    • 84988158701 scopus 로고
    • On the moving Preisach model
    • Brokate M. On the moving Preisach model. Math. Methods Appl. Sci 1992, 15(3):145-157.
    • (1992) Math. Methods Appl. Sci , vol.15 , Issue.3 , pp. 145-157
    • Brokate, M.1
  • 21
    • 0006981856 scopus 로고
    • Properties of the Preisach model for hysteresis
    • Brokate M., Visintin A. Properties of the Preisach model for hysteresis. J. Reine Angew. Math. 1989, 402:1-40.
    • (1989) J. Reine Angew. Math. , vol.402 , pp. 1-40
    • Brokate, M.1    Visintin, A.2
  • 22
    • 30844447717 scopus 로고
    • Mathematical description of the oscillations of a mass point on an elasto-plastic element
    • (in Russian), Izdat. Nauka, Moscow
    • Krasnosel'skii M.A. Mathematical description of the oscillations of a mass point on an elasto-plastic element. Partial Differential Equations (Proc. Sympos) 1970, 146-149. (in Russian), Izdat. Nauka, Moscow.
    • (1970) Partial Differential Equations (Proc. Sympos) , pp. 146-149
    • Krasnosel'skii, M.A.1
  • 23
    • 84884741222 scopus 로고
    • Operators of hysteresis nonlinearities
    • (in Russian), Izdat. Nauka Sibirsk. Otdel, Novosibirsk
    • Krasnosel'skii M.A., Pokrovskii A.V. Operators of hysteresis nonlinearities. Operator Theory in Function Space 1977, 161-187. (in Russian), Izdat. Nauka Sibirsk. Otdel, Novosibirsk.
    • (1977) Operator Theory in Function Space , pp. 161-187
    • Krasnosel'skii, M.A.1    Pokrovskii, A.V.2
  • 24
    • 84884741222 scopus 로고
    • Operators of hysteresis nonlinearities
    • (in Russian), Izdat. Nauka Sibirsk. Otdel, Novosibirsk
    • Krasnosel'skii M.A., Pokrovskii A.V. Operators of hysteresis nonlinearities. Operator Theory in Function Space 1977, 342. (in Russian), Izdat. Nauka Sibirsk. Otdel, Novosibirsk.
    • (1977) Operator Theory in Function Space , pp. 342
    • Krasnosel'skii, M.A.1    Pokrovskii, A.V.2
  • 26
    • 84908465354 scopus 로고
    • Hystérésis dans les systèmes distribués
    • Visintin A. Hystérésis dans les systèmes distribués. C.R. Acad. Sci. Paris Sér. I Math. 1981, 293(14):625-628.
    • (1981) C.R. Acad. Sci. Paris Sér. I Math. , vol.293 , Issue.14 , pp. 625-628
    • Visintin, A.1
  • 27
    • 0006912360 scopus 로고
    • A model for hysteresis of distributed systems
    • Visintin A. A model for hysteresis of distributed systems. Ann. Mat. Pura Appl. 1982, 131(4):203-231.
    • (1982) Ann. Mat. Pura Appl. , vol.131 , Issue.4 , pp. 203-231
    • Visintin, A.1
  • 28
    • 0004632667 scopus 로고
    • Aphase transition problem with delay
    • Visintin A. Aphase transition problem with delay. Control Cybernet. 1982, 11(1-2):5-18.
    • (1982) Control Cybernet. , vol.11 , Issue.1-2 , pp. 5-18
    • Visintin, A.1
  • 29
    • 0001123475 scopus 로고
    • Continuity properties of a class of hysteresis functionals
    • Visintin A. Continuity properties of a class of hysteresis functionals. Atti Sem. Mat. Fis. Univ. Modena 1983, 32(2):232-247.
    • (1983) Atti Sem. Mat. Fis. Univ. Modena , vol.32 , Issue.2 , pp. 232-247
    • Visintin, A.1
  • 30
    • 3643120241 scopus 로고
    • On the evolution of ferromagnetic media
    • Visintin A. On the evolution of ferromagnetic media. Math. Modelling 1984, 5(1):43-61.
    • (1984) Math. Modelling , vol.5 , Issue.1 , pp. 43-61
    • Visintin, A.1
  • 31
    • 0021488609 scopus 로고
    • On the Preisach model for hysteresis
    • Visintin A. On the Preisach model for hysteresis. Nonlinear Anal. 1984, 8(9):977-996.
    • (1984) Nonlinear Anal. , vol.8 , Issue.9 , pp. 977-996
    • Visintin, A.1
  • 32
    • 84884790697 scopus 로고
    • On variable hysteresis operators
    • (6)
    • Visintin A. On variable hysteresis operators. Boll. Un. Mat. Ital. B 1984, 3(6):837-857. (6).
    • (1984) Boll. Un. Mat. Ital. B , vol.3 , Issue.6 , pp. 837-857
    • Visintin, A.1
  • 33
    • 0642326525 scopus 로고
    • On hysteresis in phase transitions
    • Visintin A. On hysteresis in phase transitions. Control Cybernet. 1986, 14(1-3):297-307.
    • (1986) Control Cybernet. , vol.14 , Issue.1-3 , pp. 297-307
    • Visintin, A.1
  • 34
    • 45849134759 scopus 로고
    • Study of the eddy-current problem taking account of Hall's effects
    • Visintin A. Study of the eddy-current problem taking account of Hall's effects. Applicable Anal. 1985, 19(4):217-226.
    • (1985) Applicable Anal. , vol.19 , Issue.4 , pp. 217-226
    • Visintin, A.1
  • 35
    • 0006951734 scopus 로고
    • Evolution problems with hysteresis in the source term
    • Visintin A. Evolution problems with hysteresis in the source term. SIAM J. Math. Anal. 1986, 17(5):1113-1138.
    • (1986) SIAM J. Math. Anal. , vol.17 , Issue.5 , pp. 1113-1138
    • Visintin, A.1
  • 36
    • 0000267399 scopus 로고
    • Rheological models and hysteresis effects
    • Visintin A. Rheological models and hysteresis effects. Rend. Sem. Mat. Univ. Padova 1987, 77:213-241.
    • (1987) Rend. Sem. Mat. Univ. Padova , vol.77 , pp. 213-241
    • Visintin, A.1
  • 38
    • 0347985169 scopus 로고    scopus 로고
    • Quasilinear hyperbolic equations with hysteresis
    • Visintin A. Quasilinear hyperbolic equations with hysteresis. Ann. Inst. H. Poincaré Anal. Non Linéaire 2002, 19(4):451-476.
    • (2002) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.19 , Issue.4 , pp. 451-476
    • Visintin, A.1
  • 39
    • 0041794774 scopus 로고
    • Numerical approximation of hysteresis problems
    • Verdi C., Visintin A. Numerical approximation of hysteresis problems. IMA J. Numer. Anal. 1985, 5(4):447-463.
    • (1985) IMA J. Numer. Anal. , vol.5 , Issue.4 , pp. 447-463
    • Verdi, C.1    Visintin, A.2
  • 40
    • 0011010391 scopus 로고
    • Numerical approximation of the Preisach model for hysteresis
    • Verdi C., Visintin A. Numerical approximation of the Preisach model for hysteresis. RAIRO Modél. Math. Anal. Numér. 1989, 23(2):335-356.
    • (1989) RAIRO Modél. Math. Anal. Numér. , vol.23 , Issue.2 , pp. 335-356
    • Verdi, C.1    Visintin, A.2
  • 41
    • 0011044656 scopus 로고
    • A monotonicity method for solving hyperbolic problems with hysteresis
    • Krejcí P. A monotonicity method for solving hyperbolic problems with hysteresis. Appl. Math. 1988, 33(3):197-203.
    • (1988) Appl. Math. , vol.33 , Issue.3 , pp. 197-203
    • Krejcí, P.1
  • 42
    • 84884740410 scopus 로고
    • On Ishlinskii's model for non-perfectly elastic bodies
    • Krejcí P. On Ishlinskii's model for non-perfectly elastic bodies. Appl. Math. 1988, 33(2):133-144.
    • (1988) Appl. Math. , vol.33 , Issue.2 , pp. 133-144
    • Krejcí, P.1
  • 43
    • 0001432332 scopus 로고
    • On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case
    • Krejcí P. On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case. Appl. Math. 1989, 34(5):364-374.
    • (1989) Appl. Math. , vol.34 , Issue.5 , pp. 364-374
    • Krejcí, P.1
  • 44
    • 4243790984 scopus 로고
    • Global behavior of solutions to the wave equation with hysteresis
    • Krejcí P. Global behavior of solutions to the wave equation with hysteresis. Adv. Math. Sci. Appl. 1993, 2(1):1-23.
    • (1993) Adv. Math. Sci. Appl. , vol.2 , Issue.1 , pp. 1-23
    • Krejcí, P.1
  • 45
    • 0040927495 scopus 로고    scopus 로고
    • A remark on the local Lipschitz continuity of vector hysteresis operators
    • Krejcí P. A remark on the local Lipschitz continuity of vector hysteresis operators. Appl. Math. 2001, 46(1):1-11.
    • (2001) Appl. Math. , vol.46 , Issue.1 , pp. 1-11
    • Krejcí, P.1
  • 46
    • 0031128531 scopus 로고    scopus 로고
    • On a system of nonlinear PDEs with temperature-dependent hysteresis in one-dimensional thermoplasticity
    • Krejcí P., Sprekels J. On a system of nonlinear PDEs with temperature-dependent hysteresis in one-dimensional thermoplasticity. J. Math. Anal. Appl. 1997, 209(1):25-46.
    • (1997) J. Math. Anal. Appl. , vol.209 , Issue.1 , pp. 25-46
    • Krejcí, P.1    Sprekels, J.2
  • 47
    • 0032139904 scopus 로고    scopus 로고
    • Global solutions to a coupled parabolic-hyperbolic system with hysteresis in 1-D magnetoelasticity
    • Krejí P., Sprekels J. Global solutions to a coupled parabolic-hyperbolic system with hysteresis in 1-D magnetoelasticity. Nonlinear Anal. 1998, 33(4):341-358.
    • (1998) Nonlinear Anal. , vol.33 , Issue.4 , pp. 341-358
    • Krejí, P.1    Sprekels, J.2
  • 48
    • 0000567631 scopus 로고    scopus 로고
    • Hysteresis operators in phase-field models of Penrose-Fife type
    • Krejí P., Sprekels J. Hysteresis operators in phase-field models of Penrose-Fife type. Appl. Math. 1998, 43(3):207-222.
    • (1998) Appl. Math. , vol.43 , Issue.3 , pp. 207-222
    • Krejí, P.1    Sprekels, J.2
  • 49
    • 0034140736 scopus 로고    scopus 로고
    • A hysteresis approach to phase-field models
    • Ser. A: Theory Methods
    • Krejí P., Sprekels J. A hysteresis approach to phase-field models. Nonlinear Anal. 2000, 39(5):569-586. Ser. A: Theory Methods.
    • (2000) Nonlinear Anal. , vol.39 , Issue.5 , pp. 569-586
    • Krejí, P.1    Sprekels, J.2
  • 50
    • 84884784520 scopus 로고
    • Conditions for the existence and uniqueness of a solution of the Cauchy problem for a system of ordinary differential equations with hysteresis nonlinearities
    • I.Borzdyko V Conditions for the existence and uniqueness of a solution of the Cauchy problem for a system of ordinary differential equations with hysteresis nonlinearities. Dokl. Akad. Nauk Tadzhik. SSR 1987, 30(12):766-770.
    • (1987) Dokl. Akad. Nauk Tadzhik. SSR , vol.30 , Issue.12 , pp. 766-770
    • I.Borzdyko, V.1
  • 51
    • 84884769625 scopus 로고
    • A uniqueness theorem of S. R. Bernfeld-R. D. Driver-V. Lakshmikantham theorem type for differential equations with hysteresis nonlinearities
    • Borzdyko V.I. A uniqueness theorem of S. R. Bernfeld-R. D. Driver-V. Lakshmikantham theorem type for differential equations with hysteresis nonlinearities. Dokl. Akad. Nauk Tadzhik. SSR 1987, 30(2):74-77.
    • (1987) Dokl. Akad. Nauk Tadzhik. SSR , vol.30 , Issue.2 , pp. 74-77
    • Borzdyko, V.I.1
  • 52
    • 84884763924 scopus 로고
    • Uniqueness theorems for differential equations with hysteresis nonlinearities
    • Borzdyko V.I. Uniqueness theorems for differential equations with hysteresis nonlinearities. Differentsial'nye Uravneniya 1987, 23(6):937-941.
    • (1987) Differentsial'nye Uravneniya , vol.23 , Issue.6 , pp. 937-941
    • Borzdyko, V.I.1
  • 53
    • 84884763924 scopus 로고
    • Uniqueness theorems for differential equations with hysteresis nonlinearities
    • Borzdyko V.I. Uniqueness theorems for differential equations with hysteresis nonlinearities. Differentsial'nye Uravneniya 1987, 23(6):1100.
    • (1987) Differentsial'nye Uravneniya , vol.23 , Issue.6 , pp. 1100
    • Borzdyko, V.I.1
  • 54
    • 84884734244 scopus 로고
    • Uniqueness conditions for systems of differential equations with hysteresis terms
    • Borzdyko V.I. Uniqueness conditions for systems of differential equations with hysteresis terms. Differentsial'nye Uravneniya 1988, 24(8):1291-1295.
    • (1988) Differentsial'nye Uravneniya , vol.24 , Issue.8 , pp. 1291-1295
    • Borzdyko, V.I.1
  • 55
    • 84884734244 scopus 로고
    • Uniqueness conditions for systems of differential equations with hysteresis terms
    • Borzdyko V.I. Uniqueness conditions for systems of differential equations with hysteresis terms. Differentsial'nye Uravneniya 1988, 24(8):1468.
    • (1988) Differentsial'nye Uravneniya , vol.24 , Issue.8 , pp. 1468
    • Borzdyko, V.I.1
  • 56
    • 84884782987 scopus 로고
    • A uniqueness theorem of the type of Wend's theorem for differential equations with hysteresis nonlinearities
    • Borzdyko V.I. A uniqueness theorem of the type of Wend's theorem for differential equations with hysteresis nonlinearities. Izv. Akad. Nauk Tadzhik. SSR Otdel. Fiz.-Mat. Khim. i Geol. Nauk. 1988, 2(108):63-65.
    • (1988) Izv. Akad. Nauk Tadzhik. SSR Otdel. Fiz.-Mat. Khim. i Geol. Nauk. , vol.2 , Issue.108 , pp. 63-65
    • Borzdyko, V.I.1
  • 57
    • 84884761047 scopus 로고
    • Uniqueness conditions for differential equations with hysteresis nonlinearities
    • Borzdyko V.I. Uniqueness conditions for differential equations with hysteresis nonlinearities. Dokl. Akad. Nauk. 1992, 324(1):56-59.
    • (1992) Dokl. Akad. Nauk. , vol.324 , Issue.1 , pp. 56-59
    • Borzdyko, V.I.1
  • 58
    • 23044523117 scopus 로고    scopus 로고
    • Hysteresis in filtration through porous media
    • Bagagiolo F., Visintin A. Hysteresis in filtration through porous media. Z. Anal. Anwendungen 2000, 19(4):977-997.
    • (2000) Z. Anal. Anwendungen , vol.19 , Issue.4 , pp. 977-997
    • Bagagiolo, F.1    Visintin, A.2
  • 59
    • 0035735426 scopus 로고    scopus 로고
    • Analysis of a new model for unsaturated flow in porous media including hysteresis and dynamic effects
    • Beliaev A.Y., Schotting R.J. Analysis of a new model for unsaturated flow in porous media including hysteresis and dynamic effects. Comput. Geosci. 2001, 5(4):345-368.
    • (2001) Comput. Geosci. , vol.5 , Issue.4 , pp. 345-368
    • Beliaev, A.Y.1    Schotting, R.J.2
  • 60
    • 0027001592 scopus 로고
    • Mathematical study of the Dahl's friction model
    • 3, 6
    • Bliman P.-A. Mathematical study of the Dahl's friction model. European J. Mech. A Solids 1992, 11:835-848. 3, 6.
    • (1992) European J. Mech. A Solids , vol.11 , pp. 835-848
    • Bliman, P.-A.1
  • 62
    • 0034223902 scopus 로고    scopus 로고
    • Hysteresis in phase-field models with thermal memory
    • Gilardi G., Krejí P., Sprekels J. Hysteresis in phase-field models with thermal memory. Math. Methods Appl. Sci 2000, 23(10):909-922.
    • (2000) Math. Methods Appl. Sci , vol.23 , Issue.10 , pp. 909-922
    • Gilardi, G.1    Krejí, P.2    Sprekels, J.3
  • 63
    • 33646972941 scopus 로고    scopus 로고
    • Uniqueness theorem for a Cauchy problem with hysteresis
    • Kopfová J. Uniqueness theorem for a Cauchy problem with hysteresis. Proc. Amer. Math. Soc. 1999, 127(12):3527-3532.
    • (1999) Proc. Amer. Math. Soc. , vol.127 , Issue.12 , pp. 3527-3532
    • Kopfová, J.1
  • 64
  • 65
    • 0026942373 scopus 로고
    • On the dynamics of controlled systems described by equations of parabolic type with hysteresis nonlinearities
    • Krasnosel'skii M.A., Pokrovskii A.V., Chernorutskii V.V., Tronel Z. On the dynamics of controlled systems described by equations of parabolic type with hysteresis nonlinearities. Avtomat. i Telemekh. 1992, (11):65-71.
    • (1992) Avtomat. i Telemekh. , Issue.11 , pp. 65-71
    • Krasnosel'skii, M.A.1    Pokrovskii, A.V.2    Chernorutskii, V.V.3    Tronel, Z.4
  • 66
    • 33845252106 scopus 로고    scopus 로고
    • Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behavior of solutions
    • (Electronic)
    • Logemann H., Ryan E.P. Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behavior of solutions. ESAIM Control Optim. Calc. Var. 2003, 9:169-196. (Electronic).
    • (2003) ESAIM Control Optim. Calc. Var. , vol.9 , pp. 169-196
    • Logemann, H.1    Ryan, E.P.2
  • 67
    • 25144466101 scopus 로고    scopus 로고
    • Ordinary differential systems describing hysteresis effects and numerical simulations
    • Minchev E., Okazaki T., Kenmochi N. Ordinary differential systems describing hysteresis effects and numerical simulations. Abstr. Appl. Anal. 2002, 7(11):563-583.
    • (2002) Abstr. Appl. Anal. , vol.7 , Issue.11 , pp. 563-583
    • Minchev, E.1    Okazaki, T.2    Kenmochi, N.3
  • 68
    • 84884782551 scopus 로고
    • On existence proof in plasticity theory
    • /81
    • Miyoshi T. On existence proof in plasticity theory. Kumamoto J. Sci. (Math.) 1980, 14(1):18-33. /81.
    • (1980) Kumamoto J. Sci. (Math.) , vol.14 , Issue.1 , pp. 18-33
    • Miyoshi, T.1
  • 69
    • 84884740180 scopus 로고    scopus 로고
    • On the Cauchy problem for differential equations with Mroz hysteresis nonlinearity
    • Rachinskii D.I. On the Cauchy problem for differential equations with Mroz hysteresis nonlinearity. Differ. Uravn. 1997, 33(8):1041-1048.
    • (1997) Differ. Uravn. , vol.33 , Issue.8 , pp. 1041-1048
    • Rachinskii, D.I.1
  • 70
    • 84884740180 scopus 로고    scopus 로고
    • On the Cauchy problem for differential equations with Mroz hysteresis nonlinearity
    • Rachinskii D.I. On the Cauchy problem for differential equations with Mroz hysteresis nonlinearity. Differ. Uravn. 1997, 33(8):1150.
    • (1997) Differ. Uravn. , vol.33 , Issue.8 , pp. 1150
    • Rachinskii, D.I.1
  • 72
    • 84884771371 scopus 로고
    • Forced oscillations in systems with hysteresis nonlinearities
    • Krasnosel'skii A.M. Forced oscillations in systems with hysteresis nonlinearities. Dokl. Akad. Nauk SSSR 1987, 292(5):1078-1082.
    • (1987) Dokl. Akad. Nauk SSSR , vol.292 , Issue.5 , pp. 1078-1082
    • Krasnosel'skii, A.M.1
  • 74
    • 0040175166 scopus 로고
    • Operators of a problem on forced oscillations in systems with hysteresis
    • Krasnosel'skii M.A., Pokrovskii A.V. Operators of a problem on forced oscillations in systems with hysteresis. Dokl. Akad. Nauk SSSR 1991, 319(4):819-822.
    • (1991) Dokl. Akad. Nauk SSSR , vol.319 , Issue.4 , pp. 819-822
    • Krasnosel'skii, M.A.1    Pokrovskii, A.V.2
  • 75
    • 84884806844 scopus 로고
    • Limiting periodicity of automatic control systems with hysteresis nonlinearities
    • Vladimirov A.A. Limiting periodicity of automatic control systems with hysteresis nonlinearities. Avtomat. i Telemekh. 1984, 4:26-30.
    • (1984) Avtomat. i Telemekh. , vol.4 , pp. 26-30
    • Vladimirov, A.A.1
  • 76
    • 0040891103 scopus 로고
    • Hysteresis systems with variable characteristics
    • Chernorutskii V.V., Krasnosel'skii M.A. Hysteresis systems with variable characteristics. Nonlinear Anal. 1992, 18(6):543-557.
    • (1992) Nonlinear Anal. , vol.18 , Issue.6 , pp. 543-557
    • Chernorutskii, V.V.1    Krasnosel'skii, M.A.2
  • 78
    • 0040610394 scopus 로고    scopus 로고
    • The Popov criterion in problems of forced oscillations in control systems
    • Bliman P-A., Krasnosel'skii A.M. The Popov criterion in problems of forced oscillations in control systems. Avtomat. i Telemekh. 1998, (4):3-14.
    • (1998) Avtomat. i Telemekh. , Issue.4 , pp. 3-14
    • Bliman, P.-A.1    Krasnosel'skii, A.M.2
  • 79
    • 0000453608 scopus 로고
    • Hysteresis and periodic solutions of semilinear and quasilinear wave equations
    • Krejí P. Hysteresis and periodic solutions of semilinear and quasilinear wave equations. Math. Z. 1986, 193(2):247-264.
    • (1986) Math. Z. , vol.193 , Issue.2 , pp. 247-264
    • Krejí, P.1
  • 80
    • 27744518166 scopus 로고
    • Periodic solutions to a parabolic equation with hysteresis
    • Krejí P. Periodic solutions to a parabolic equation with hysteresis. Math. Z. 1987, 194(1):61-70.
    • (1987) Math. Z. , vol.194 , Issue.1 , pp. 61-70
    • Krejí, P.1
  • 81
    • 0009705988 scopus 로고
    • Hysteresis memory preserving operators
    • Krejí P. Hysteresis memory preserving operators. Appl. Math. 1991, 36(4):305-326.
    • (1991) Appl. Math. , vol.36 , Issue.4 , pp. 305-326
    • Krejí, P.1
  • 82
    • 0038199181 scopus 로고    scopus 로고
    • Resonance in Preisach systems
    • Krejci P. Resonance in Preisach systems. Appl. Math. 2000, 45(6):439-468.
    • (2000) Appl. Math. , vol.45 , Issue.6 , pp. 439-468
    • Krejci, P.1
  • 83
    • 0036885433 scopus 로고    scopus 로고
    • Reliable solutions to the problem of periodic oscillations of an elastoplastic beam
    • Krejci P. Reliable solutions to the problem of periodic oscillations of an elastoplastic beam. Internat. J. Non-Linear Mech. 2002, 37(8):1337-1349.
    • (2002) Internat. J. Non-Linear Mech. , vol.37 , Issue.8 , pp. 1337-1349
    • Krejci, P.1
  • 84
    • 84884777349 scopus 로고
    • Die nichtlineare Theorie der inneren Reibung
    • Babuska I. Die nichtlineare Theorie der inneren Reibung. , Appl. Math. 1959, 4:303-321.
    • (1959) , Appl. Math. , vol.4 , pp. 303-321
    • Babuska, I.1
  • 85
    • 0034156975 scopus 로고    scopus 로고
    • Study of some rheological models with a finite number of degrees of freedom
    • Bastien J., Schatzman M., Lamarque C.-H. Study of some rheological models with a finite number of degrees of freedom. Eur. J. Mech. A Solids 2000, 19(2):277-307.
    • (2000) Eur. J. Mech. A Solids , vol.19 , Issue.2 , pp. 277-307
    • Bastien, J.1    Schatzman, M.2    Lamarque, C.-H.3
  • 86
    • 84915417262 scopus 로고
    • Periodic solutions of forced systems having hysteresis
    • Block H.D. Periodic solutions of forced systems having hysteresis. IRE Trans. 1960, CT-7:423-431.
    • (1960) IRE Trans. , vol.7 , pp. 423-431
    • Block, H.D.1
  • 87
    • 0037488558 scopus 로고    scopus 로고
    • Asymptotically stable oscillations in systems with hysteresis nonlinearities
    • Brokate M., Pokrovskii A.V. Asymptotically stable oscillations in systems with hysteresis nonlinearities. J. Differential Equations 1998, 150(1):98-123.
    • (1998) J. Differential Equations , vol.150 , Issue.1 , pp. 98-123
    • Brokate, M.1    Pokrovskii, A.V.2
  • 88
    • 29744452342 scopus 로고
    • The dynamics of phase locking and points of resonance in a forced magnetic oscillator
    • Bryant P., Jeffries C. The dynamics of phase locking and points of resonance in a forced magnetic oscillator. Phys. D 1987, 25(1-3):196-232.
    • (1987) Phys. D , vol.25 , Issue.1-3 , pp. 196-232
    • Bryant, P.1    Jeffries, C.2
  • 89
    • 0012743046 scopus 로고    scopus 로고
    • Homogenization of diffusion equation with scalar hysteresis operator
    • Proceedings of Partial Differential Equations and Applications
    • Franc J. Homogenization of diffusion equation with scalar hysteresis operator. Math. Bohem 2001, vol. 126:363-377.
    • (2001) Math. Bohem , vol.126 , pp. 363-377
    • Franc, J.1
  • 90
    • 84884763809 scopus 로고
    • The dynamics of a system with nonlinearity of the type of a triangular hysteresis loop
    • Klimov V.G. The dynamics of a system with nonlinearity of the type of a triangular hysteresis loop. Izv. Vyss. U?ebn. Zaved. Radiofizika 1969, 12:1024-1036.
    • (1969) Izv. Vyss. U?ebn. Zaved. Radiofizika , vol.12 , pp. 1024-1036
    • Klimov, V.G.1
  • 91
    • 0043119703 scopus 로고
    • Periodic oscillations in systems with hysteresis
    • Macki J.W., Nistri P., Zecca P. Periodic oscillations in systems with hysteresis. Rocky Mountain J. Math. 1992, 22(2):669-681.
    • (1992) Rocky Mountain J. Math. , vol.22 , Issue.2 , pp. 669-681
    • Macki, J.W.1    Nistri, P.2    Zecca, P.3
  • 93
    • 84884758737 scopus 로고
    • A new type of complete phase locking in the model of phase transition with hysteresis
    • Yagisawa K., Kambara T., Fuchikami N., Naito M. A new type of complete phase locking in the model of phase transition with hysteresis. I. Bull. Univ. Electro-Comm. 1995, 8(1):83-87.
    • (1995) I. Bull. Univ. Electro-Comm. , vol.8 , Issue.1 , pp. 83-87
    • Yagisawa, K.1    Kambara, T.2    Fuchikami, N.3    Naito, M.4
  • 94
    • 14844343214 scopus 로고
    • Frequency conditions of oscillations in nonlinear control systems with one single-valued or hysteresis-type nonlinearity
    • Yakubovich V.A. Frequency conditions of oscillations in nonlinear control systems with one single-valued or hysteresis-type nonlinearity. Avtomat. i Telemeh. 1975, (12):51-64.
    • (1975) Avtomat. i Telemeh. , Issue.12 , pp. 51-64
    • Yakubovich, V.A.1
  • 95
    • 0024085076 scopus 로고
    • Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part
    • Yakubovich V.A. Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part. Systems Control Lett. 1988, 11(3):221-228.
    • (1988) Systems Control Lett. , vol.11 , Issue.3 , pp. 221-228
    • Yakubovich, V.A.1
  • 96
    • 84884755683 scopus 로고
    • On the existence of self-induced oscillations in the two-phase Stefan problem with the simplest hysteresis operator in the boundary conditions
    • Getts I.G., Hoffmann K.-H., Meirmanov A.M. On the existence of self-induced oscillations in the two-phase Stefan problem with the simplest hysteresis operator in the boundary conditions. Dinamika Sploshn. Sredy 1993, 107:49-57.
    • (1993) Dinamika Sploshn. Sredy , vol.107 , pp. 49-57
    • Getts, I.G.1    Hoffmann, K.-H.2    Meirmanov, A.M.3
  • 97
    • 84884755683 scopus 로고
    • On the existence of self-induced oscillations in the two-phase Stefan problem with the simplest hysteresis operator in the boundary conditions
    • Getts I.G., Hoffmann K.-H., Meirmanov A.M. On the existence of self-induced oscillations in the two-phase Stefan problem with the simplest hysteresis operator in the boundary conditions. Dinamika Sploshn. Sredy 1993, 107:199.
    • (1993) Dinamika Sploshn. Sredy , vol.107 , pp. 199
    • Getts, I.G.1    Hoffmann, K.-H.2    Meirmanov, A.M.3
  • 98
    • 84884755683 scopus 로고
    • On the existence of self-induced oscillations in the two-phase Stefan problem with the simplest hysteresis operator in the boundary conditions
    • Getts I.G., Hoffmann K.-H., Meirmanov A.M. On the existence of self-induced oscillations in the two-phase Stefan problem with the simplest hysteresis operator in the boundary conditions. Dinamika Sploshn. Sredy 1993, 107:204.
    • (1993) Dinamika Sploshn. Sredy , vol.107 , pp. 204
    • Getts, I.G.1    Hoffmann, K.-H.2    Meirmanov, A.M.3
  • 99
    • 70349221203 scopus 로고
    • Periodic solutions of the Stefan problem with hysteresis-type boundary conditions
    • Götz I.G., Hoffmann K.-H., Meirmanov A.M. Periodic solutions of the Stefan problem with hysteresis-type boundary conditions. Manuscripta Math. 1993, 78(2):179-199.
    • (1993) Manuscripta Math. , vol.78 , Issue.2 , pp. 179-199
    • Götz, I.G.1    Hoffmann, K.-H.2    Meirmanov, A.M.3
  • 100
    • 0007219448 scopus 로고
    • Asymptotic stability for nonlinear PDEs with hysteresis
    • Kenmochi N., Visintin A. Asymptotic stability for nonlinear PDEs with hysteresis. European J. Appl. Math. 1994, 5(1):39-56.
    • (1994) European J. Appl. Math. , vol.5 , Issue.1 , pp. 39-56
    • Kenmochi, N.1    Visintin, A.2
  • 102
    • 0345980208 scopus 로고    scopus 로고
    • Asymptotic stability of large-amplitude oscillations in systems with hysteresis
    • Rachinskii D. Asymptotic stability of large-amplitude oscillations in systems with hysteresis. NoDEA Nonlinear Differential Equations Appl. 1999, 6(3):267-288.
    • (1999) NoDEA Nonlinear Differential Equations Appl. , vol.6 , Issue.3 , pp. 267-288
    • Rachinskii, D.1
  • 104
    • 0030870261 scopus 로고    scopus 로고
    • Forced oscillations of pendant (sessile) drops
    • Wilkes E.D., Basaran O.A. Forced oscillations of pendant (sessile) drops. Phys. Fluids 1997, 9(6):1512-1528.
    • (1997) Phys. Fluids , vol.9 , Issue.6 , pp. 1512-1528
    • Wilkes, E.D.1    Basaran, O.A.2
  • 105
    • 84884760338 scopus 로고
    • Self-oscillations in systems with hysteresis
    • Zubov S.V. Self-oscillations in systems with hysteresis. Mat. Fiz. (Vyp. 20) 1976, 31.
    • (1976) Mat. Fiz. (Vyp. 20) , pp. 31
    • Zubov, S.V.1
  • 106
    • 84884760338 scopus 로고
    • Self-oscillations in systems with hysteresis
    • Zubov S.V. Self-oscillations in systems with hysteresis. Mat. Fiz. (Vyp. 20) 1976, 33.
    • (1976) Mat. Fiz. (Vyp. 20) , pp. 33
    • Zubov, S.V.1
  • 107
    • 84884760338 scopus 로고
    • Self-oscillations in systems with hysteresis
    • Zubov S.V. Self-oscillations in systems with hysteresis. Mat. Fiz. (Vyp. 20) 1976, 112.
    • (1976) Mat. Fiz. (Vyp. 20) , pp. 112
    • Zubov, S.V.1
  • 108
    • 84884766643 scopus 로고
    • Stability of periodic solutions of relay systems with hysteresis
    • Anapol'skiy L.Y., Petryakova Y.A. Stability of periodic solutions of relay systems with hysteresis. Automatika 1985, (1):79-82.
    • (1985) Automatika , Issue.1 , pp. 79-82
    • Anapol'skiy, L.Y.1    Petryakova, Y.A.2
  • 109
    • 84884766643 scopus 로고
    • Stability of periodic solutions of relay systems with hysteresis
    • Anapol'skiy L.Y., Petryakova Y.A. Stability of periodic solutions of relay systems with hysteresis. Automatika 1985, (1):97.
    • (1985) Automatika , Issue.1 , pp. 97
    • Anapol'skiy, L.Y.1    Petryakova, Y.A.2
  • 110
    • 34547113722 scopus 로고    scopus 로고
    • Periodic solutions in systems at resonances with small relay hysteresis
    • Feckan M. Periodic solutions in systems at resonances with small relay hysteresis. Math. Slovaca 1999, 49(1):41-52.
    • (1999) Math. Slovaca , vol.49 , Issue.1 , pp. 41-52
    • Feckan, M.1
  • 111
    • 70349911368 scopus 로고
    • Existence and uniqueness of the periodic solution of a relay system with hysteresis
    • Kamakin A.M. Existence and uniqueness of the periodic solution of a relay system with hysteresis. Differencial'nye Uravnenija 1972, 8:1505-1506.
    • (1972) Differencial'nye Uravnenija , vol.8 , pp. 1505-1506
    • Kamakin, A.M.1
  • 112
    • 0035995793 scopus 로고    scopus 로고
    • Differential equations, hysteresis, and time delay
    • Kopfová J., Kopf T. Differential equations, hysteresis, and time delay. Z. Angew. Math. Phys. 2002, 53(4):676-691.
    • (2002) Z. Angew. Math. Phys. , vol.53 , Issue.4 , pp. 676-691
    • Kopfová, J.1    Kopf, T.2
  • 113
    • 0027555225 scopus 로고
    • Mathematical models for hysteresis
    • Macki J.W., Nistri P., Zecca P. Mathematical models for hysteresis. SIAM Rev. 1993, 35(1):94-123.
    • (1993) SIAM Rev. , vol.35 , Issue.1 , pp. 94-123
    • Macki, J.W.1    Nistri, P.2    Zecca, P.3
  • 114
    • 84884735668 scopus 로고
    • A system with hysteresis
    • Zubov S.V. A system with hysteresis. Differentsial'nye Uravneniya 1978, 14(6):1133-1135.
    • (1978) Differentsial'nye Uravneniya , vol.14 , Issue.6 , pp. 1133-1135
    • Zubov, S.V.1
  • 115
  • 116
    • 84884736852 scopus 로고
    • Stability of periodic modes of relay systems with hysteresis
    • Zubov S.V. Stability of periodic modes of relay systems with hysteresis. Mat. Fiz. 1979, 25.
    • (1979) Mat. Fiz. , pp. 25
    • Zubov, S.V.1
  • 117
    • 84884736852 scopus 로고
    • Stability of periodic modes of relay systems with hysteresis
    • Zubov S.V. Stability of periodic modes of relay systems with hysteresis. Mat. Fiz. 1979, 30-35.
    • (1979) Mat. Fiz. , pp. 30-35
    • Zubov, S.V.1
  • 118
    • 84884736852 scopus 로고
    • Stability of periodic modes of relay systems with hysteresis
    • Zubov S.V. Stability of periodic modes of relay systems with hysteresis. Mat. Fiz. 1979, 118.
    • (1979) Mat. Fiz. , pp. 118
    • Zubov, S.V.1
  • 119
    • 26444529547 scopus 로고    scopus 로고
    • Asymptotically stable almost-periodic oscillations in systems with hysteresis nonlinearities
    • Brokate M., Collings I., Pokrovskii A.V., Stagnitti F. Asymptotically stable almost-periodic oscillations in systems with hysteresis nonlinearities. Z. Anal. Anwendungen 2000, 19(2):469-487.
    • (2000) Z. Anal. Anwendungen , vol.19 , Issue.2 , pp. 469-487
    • Brokate, M.1    Collings, I.2    Pokrovskii, A.V.3    Stagnitti, F.4
  • 122
    • 0031334629 scopus 로고    scopus 로고
    • On the correspondence between micromechanical models for isothermal pseudoelastic response of shape memory alloys and the Preisach model for hysteresis
    • Lagoudas D.C., Bhattacharyya A. On the correspondence between micromechanical models for isothermal pseudoelastic response of shape memory alloys and the Preisach model for hysteresis. Math. Mech. Solids 1997, 2(4):405-440.
    • (1997) Math. Mech. Solids , vol.2 , Issue.4 , pp. 405-440
    • Lagoudas, D.C.1    Bhattacharyya, A.2
  • 123
    • 84983945763 scopus 로고
    • Resonance in a rigid rotor with elastic support
    • Ruijgrok M., Tondl A., Verhulst F. Resonance in a rigid rotor with elastic support. Z. Angew. Math. Mech. 1993, 73(10):255-263.
    • (1993) Z. Angew. Math. Mech. , vol.73 , Issue.10 , pp. 255-263
    • Ruijgrok, M.1    Tondl, A.2    Verhulst, F.3
  • 124
    • 84884766602 scopus 로고
    • Averaging properties of multidimensional hysteresis operators
    • Vladimirov A.A. Averaging properties of multidimensional hysteresis operators. Dokl. Akad. Nauk SSSR 1989, 309(6):1289-1292.
    • (1989) Dokl. Akad. Nauk SSSR , vol.309 , Issue.6 , pp. 1289-1292
    • Vladimirov, A.A.1
  • 125
    • 84884809141 scopus 로고
    • The application of the averaging method to the calculation of the oscillations of nonlinear systems while taking into account the scattering of energy
    • Volosov V.M., Morgunov B.I. The application of the averaging method to the calculation of the oscillations of nonlinear systems while taking into account the scattering of energy. Vestnik Moskov. Univ. Ser. III Fiz. Astronom. 1972, 27(2):238-240.
    • (1972) Vestnik Moskov. Univ. Ser. III Fiz. Astronom. , vol.27 , Issue.2 , pp. 238-240
    • Volosov, V.M.1    Morgunov, B.I.2
  • 126
    • 0037182666 scopus 로고    scopus 로고
    • Stochastic averaging of Duhem hysteretic systems
    • Ying Z.G., Zhu W.Q., Ni Y.Q., Ko J.M. Stochastic averaging of Duhem hysteretic systems. J. Sound Vibration 2002, 254(1):91-104.
    • (2002) J. Sound Vibration , vol.254 , Issue.1 , pp. 91-104
    • Ying, Z.G.1    Zhu, W.Q.2    Ni, Y.Q.3    Ko, J.M.4
  • 127
    • 0000214070 scopus 로고    scopus 로고
    • Homogenization of scalar wave equations with hysteresis
    • Franc J., Krejí P. Homogenization of scalar wave equations with hysteresis. Contin. Mech. Thermodyn. 1999, 11(6):371-390.
    • (1999) Contin. Mech. Thermodyn. , vol.11 , Issue.6 , pp. 371-390
    • Franc, J.1    Krejí, P.2
  • 128
    • 84884739271 scopus 로고
    • Forced oscillations of an oscillator with account taken of hysteresis
    • Gilman T.S., V Polrovskii A. Forced oscillations of an oscillator with account taken of hysteresis. Dokl. Akad. Nauk SSSR 1982, 263(4):790-793.
    • (1982) Dokl. Akad. Nauk SSSR , vol.263 , Issue.4 , pp. 790-793
    • Gilman, T.S.1    Polrovskii, A.2
  • 130
    • 0035774065 scopus 로고    scopus 로고
    • On the continua of cycles in systems with hysteresis
    • Krasnosel'skii A.M., Rachinskii D.I. On the continua of cycles in systems with hysteresis. Dokl. Akad. Nauk 2001, 378(3):314-319.
    • (2001) Dokl. Akad. Nauk , vol.378 , Issue.3 , pp. 314-319
    • Krasnosel'skii, A.M.1    Rachinskii, D.I.2
  • 131
    • 84884739903 scopus 로고
    • Dynamics of the angular motion of an aircraft in the presence of aerodynamic hysteresis of the moment characteristic
    • Bogodistov S.S., G.Sitnikov V Dynamics of the angular motion of an aircraft in the presence of aerodynamic hysteresis of the moment characteristic. Uchen. Zap. TsAGI 1987, 18(2):130-142.
    • (1987) Uchen. Zap. TsAGI , vol.18 , Issue.2 , pp. 130-142
    • Bogodistov, S.S.1    G.Sitnikov, V.2
  • 132
    • 9344246189 scopus 로고    scopus 로고
    • Bifurcation of periodic and chaotic solutions in discontinuous systems
    • Equadiff9, Brno, 1
    • Fekan M. Bifurcation of periodic and chaotic solutions in discontinuous systems. Arch. Math. (Brno) 1998, 34:73-82. Equadiff9, Brno, 1.
    • (1998) Arch. Math. (Brno) , vol.34 , pp. 73-82
    • Fekan, M.1
  • 133
    • 0001942632 scopus 로고
    • Thermomechanical description of pseudoelasticity -the threshold-type dissipative force with discrete memory
    • 1997
    • Levitas V.I. Thermomechanical description of pseudoelasticity -the threshold-type dissipative force with discrete memory. Mech. Res. Comm. 1994, 21(3):273-280. 1997.
    • (1994) Mech. Res. Comm. , vol.21 , Issue.3 , pp. 273-280
    • Levitas, V.I.1
  • 134
    • 0026371184 scopus 로고
    • A method for numerical analysis of bifurcation of periodic solutions in nonautonomous systems with hysteretic elements
    • Matsuo T., Kishima A. A method for numerical analysis of bifurcation of periodic solutions in nonautonomous systems with hysteretic elements. Electron. Comm. Japan Part III Fund. Electron. Sci. 1991, 74(12):33-42.
    • (1991) Electron. Comm. Japan Part III Fund. Electron. Sci. , vol.74 , Issue.12 , pp. 33-42
    • Matsuo, T.1    Kishima, A.2
  • 135
    • 0032647268 scopus 로고    scopus 로고
    • Bifurcation and metastability in a new one-dimensional model for martensitic phase transitions
    • 3-4, Computational methods and bifurcation theory with applications
    • Vainchtein A., Healey T.J., Rosakis P. Bifurcation and metastability in a new one-dimensional model for martensitic phase transitions. Comput. Methods Appl. Mech. Engrg. 1999, 170:407-421. 3-4.
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.170 , pp. 407-421
    • Vainchtein, A.1    Healey, T.J.2    Rosakis, P.3
  • 136
    • 0036337739 scopus 로고    scopus 로고
    • Two-dimensional bifurcation diagrams of a chaotic circuit based on hysteresis
    • Bizzarri F., Storace M. Two-dimensional bifurcation diagrams of a chaotic circuit based on hysteresis. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 2002, 12(1):43-69.
    • (2002) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.12 , Issue.1 , pp. 43-69
    • Bizzarri, F.1    Storace, M.2
  • 137
    • 35949019955 scopus 로고
    • Bifurcations of a forced magnetic oscillator near points of resonance
    • Bryant P., Jeffries C. Bifurcations of a forced magnetic oscillator near points of resonance. Phys. Rev. Lett. 1984, 53(3):250-253.
    • (1984) Phys. Rev. Lett. , vol.53 , Issue.3 , pp. 250-253
    • Bryant, P.1    Jeffries, C.2
  • 138
    • 0011313328 scopus 로고
    • Chaotic motion and its probabilistic description in a family of two-dimensional nonlinear systems with hysteresis
    • Feng X., Loparo K.A. Chaotic motion and its probabilistic description in a family of two-dimensional nonlinear systems with hysteresis. J. Nonlinear Sci. 1992, 2(4):417-452.
    • (1992) J. Nonlinear Sci. , vol.2 , Issue.4 , pp. 417-452
    • Feng, X.1    Loparo, K.A.2
  • 139
    • 0004796974 scopus 로고
    • Devil's attractors and chaos of a driven impact oscillator
    • Isomäki H.M., Von Boehm J., Räty R. Devil's attractors and chaos of a driven impact oscillator. Phys. Lett. A 1985, 107(8):343-346.
    • (1985) Phys. Lett. A , vol.107 , Issue.8 , pp. 343-346
    • Isomäki, H.M.1    Von Boehm, J.2    Räty, R.3
  • 140
    • 0026915170 scopus 로고
    • Numerical analysis of bifurcations in Duffing's equation with hysteretic functions
    • Matsuo T., Kishima A. Numerical analysis of bifurcations in Duffing's equation with hysteretic functions. Electron. Comm. Japan Part III Fund. Electron. Sci. 1992, 75(9):61-71.
    • (1992) Electron. Comm. Japan Part III Fund. Electron. Sci. , vol.75 , Issue.9 , pp. 61-71
    • Matsuo, T.1    Kishima, A.2
  • 141
    • 0032026692 scopus 로고    scopus 로고
    • Stochasticity of relay systems with hysteresis
    • Postnikov N.S. Stochasticity of relay systems with hysteresis. Avtomat. i Telemekh. 1998, (3):57-68.
    • (1998) Avtomat. i Telemekh. , Issue.3 , pp. 57-68
    • Postnikov, N.S.1
  • 142
    • 0035768444 scopus 로고    scopus 로고
    • Chaotic oscillations in a relay system with hysteresis
    • Zhusubaliev Z.T., Titov V.S. Chaotic oscillations in a relay system with hysteresis. Avtomat. i Telemekh. 2001, (1):67-79.
    • (2001) Avtomat. i Telemekh. , Issue.1 , pp. 67-79
    • Zhusubaliev, Z.T.1    Titov, V.S.2
  • 143
    • 0029402723 scopus 로고
    • Robustness of the observable behavior of semihyperbolic dynamical systems
    • Daimond F., Kloeden P., Kozyakin V.S., Pokrovskii A.V. Robustness of the observable behavior of semihyperbolic dynamical systems. Avtomat. i Telemekh. 1995, (11):148-159.
    • (1995) Avtomat. i Telemekh. , Issue.11 , pp. 148-159
    • Daimond, F.1    Kloeden, P.2    Kozyakin, V.S.3    Pokrovskii, A.V.4
  • 145
    • 0036885425 scopus 로고    scopus 로고
    • Optimal control of dynamical systems with Preisach hysteresis
    • Belbas S.A., Mayergoyz I.D. Optimal control of dynamical systems with Preisach hysteresis. Internat. J. Non-Linear Mech. 2002, 37(8):1351-1361.
    • (2002) Internat. J. Non-Linear Mech. , vol.37 , Issue.8 , pp. 1351-1361
    • Belbas, S.A.1    Mayergoyz, I.D.2
  • 146
    • 0024705845 scopus 로고
    • Optimal design for heat conduction problems with hysteresis
    • Brokate M., Friedman A. Optimal design for heat conduction problems with hysteresis. SIAM J. Control Optim. 1989, 27(4):697-717.
    • (1989) SIAM J. Control Optim. , vol.27 , Issue.4 , pp. 697-717
    • Brokate, M.1    Friedman, A.2
  • 147
    • 0024882228 scopus 로고
    • Existence and optimal control of mechanical processes with hysteresis in viscous solids
    • Brokate M., Sprekels J. Existence and optimal control of mechanical processes with hysteresis in viscous solids. IMA J. Appl. Math. 1989, 43(3):219-229.
    • (1989) IMA J. Appl. Math. , vol.43 , Issue.3 , pp. 219-229
    • Brokate, M.1    Sprekels, J.2
  • 148
    • 0347648899 scopus 로고    scopus 로고
    • Automatic control problems for reaction-diffusion systems
    • Cavaterra C., Colombo F. Automatic control problems for reaction-diffusion systems. J. Evol. Equ. 2002, 2(2):241-273.
    • (2002) J. Evol. Equ. , vol.2 , Issue.2 , pp. 241-273
    • Cavaterra, C.1    Colombo, F.2
  • 149
    • 26444605023 scopus 로고    scopus 로고
    • Automatic control of the temperature in phase change prob-lems with memory
    • Gatti S. Automatic control of the temperature in phase change prob-lems with memory. Z. Anal. Anwendungen 2001, 20(4):883-914.
    • (2001) Z. Anal. Anwendungen , vol.20 , Issue.4 , pp. 883-914
    • Gatti, S.1
  • 150
    • 0033228194 scopus 로고    scopus 로고
    • Automatic control of the temperature in thermovisco-elasticity
    • Grasselli M. Automatic control of the temperature in thermovisco-elasticity. Math. Methods Appl. Sci 1999, 22(16):1447-1464.
    • (1999) Math. Methods Appl. Sci , vol.22 , Issue.16 , pp. 1447-1464
    • Grasselli, M.1
  • 152
    • 84884806803 scopus 로고
    • Simulation of transformers with hysteresis by means of continual relay systems
    • Krasnosel'skii M.A., Pokrovskii A.V. Simulation of transformers with hysteresis by means of continual relay systems. Dokl. Akad. Nauk SSSR 1976, 227(3):547-550.
    • (1976) Dokl. Akad. Nauk SSSR , vol.227 , Issue.3 , pp. 547-550
    • Krasnosel'skii, M.A.1    Pokrovskii, A.V.2
  • 153
    • 0031678177 scopus 로고    scopus 로고
    • Hysteresis modeling in magnetostrictive materials via Preisach operators
    • 23 pp.
    • Smith R.C. Hysteresis modeling in magnetostrictive materials via Preisach operators. J. Math. Systems Estim. Control 1998, 8(2). 23 pp.
    • (1998) J. Math. Systems Estim. Control , vol.8 , Issue.2
    • Smith, R.C.1
  • 154
    • 0033102036 scopus 로고    scopus 로고
    • Automatic control via thermostats of a hyperbolic Stefan problem with memory
    • Colli P., Grasselli M., Sprekels J. Automatic control via thermostats of a hyperbolic Stefan problem with memory. Appl. Math. Optim. 1999, 39(2):229-255.
    • (1999) Appl. Math. Optim. , vol.39 , Issue.2 , pp. 229-255
    • Colli, P.1    Grasselli, M.2    Sprekels, J.3
  • 155
    • 0033588768 scopus 로고    scopus 로고
    • The stop operator related to a convex polyhedron
    • Desch W., Turi J. The stop operator related to a convex polyhedron. J. Differential Equations 1999, 157(2):329-347.
    • (1999) J. Differential Equations , vol.157 , Issue.2 , pp. 329-347
    • Desch, W.1    Turi, J.2
  • 156
    • 0032118359 scopus 로고    scopus 로고
    • Complementary 2-D finite element procedures for the magnetic field analysis using a vector hysteresis model
    • Dupré L.R., Van Keer R., Melkebeek J.A.A. Complementary 2-D finite element procedures for the magnetic field analysis using a vector hysteresis model. Int. J. Numer. Methods Engrg. 1998, 42(6):1005-1023.
    • (1998) Int. J. Numer. Methods Engrg. , vol.42 , Issue.6 , pp. 1005-1023
    • Dupré, L.R.1    Van Keer, R.2    Melkebeek, J.A.A.3
  • 157
    • 84884764454 scopus 로고
    • The absolute stability of systems with several nonlinear components
    • Krasnosel'skii M.A., Pokrovskii A.V. The absolute stability of systems with several nonlinear components. Dokl. Akad. Nauk SSSR 1983, 271(6):1314-1316.
    • (1983) Dokl. Akad. Nauk SSSR , vol.271 , Issue.6 , pp. 1314-1316
    • Krasnosel'skii, M.A.1    Pokrovskii, A.V.2
  • 159
    • 0003501055 scopus 로고
    • (Translated from the Russian by A. Libin, translation edited by D. Louvish), Halsted Press (A division of John Wiley & Sons), New York, Toronto
    • Krasnosel'skii M.A., Burd V.S., Kolesov Y.S. Nonlinear Almost Periodic Oscillations 1973, (Translated from the Russian by A. Libin, translation edited by D. Louvish), Halsted Press (A division of John Wiley & Sons), New York, Toronto.
    • (1973) Nonlinear Almost Periodic Oscillations
    • Krasnosel'skii, M.A.1    Burd, V.S.2    Kolesov, Y.S.3
  • 163
    • 84884743216 scopus 로고
    • The limit norm of a linear operator and its applications
    • Pokrovskii A.V. The limit norm of a linear operator and its applications. Dokl. Akad. Nauk SSSR 1979, 249(3):548-551.
    • (1979) Dokl. Akad. Nauk SSSR , vol.249 , Issue.3 , pp. 548-551
    • Pokrovskii, A.V.1
  • 164
    • 84884810006 scopus 로고
    • Limit norm of a linear element
    • Pokrovskii A.V. Limit norm of a linear element. Avtomat. i Telemekh. 1985, (11):62-69.
    • (1985) Avtomat. i Telemekh. , Issue.11 , pp. 62-69
    • Pokrovskii, A.V.1
  • 165
    • 84884742909 scopus 로고
    • Stable periodic regimes in control systems with monotone nonlinearities
    • Pokrovskii A.V., Semenov M.E. Stable periodic regimes in control systems with monotone nonlinearities. Avtomat. i Telemekh. 1990, (2):31-37.
    • (1990) Avtomat. i Telemekh. , Issue.2 , pp. 31-37
    • Pokrovskii, A.V.1    Semenov, M.E.2
  • 166
    • 0003712688 scopus 로고
    • The Operator of Translation Along the Trajectories of Differential Equations
    • Translated from the Russian by Scrip ta Technica, American Mathematical Society, Providence, RI
    • Krasnosel'skii M.A. The Operator of Translation Along the Trajectories of Differential Equations. Translations of Mathematical Monographs 1968, Vol. 19. Translated from the Russian by Scrip ta Technica, American Mathematical Society, Providence, RI.
    • (1968) Translations of Mathematical Monographs , vol.19
    • Krasnosel'skii, M.A.1
  • 167
    • 26444584678 scopus 로고
    • Shuttle algorithm in investigation of systems with hysteresis nonlinearities
    • Trento, 1991, Longman Sci. Tech., Harlow
    • Pokrovskii A. Shuttle algorithm in investigation of systems with hysteresis nonlinearities. Models of Hysteresis 1993, 124-142. Trento, 1991, Longman Sci. Tech., Harlow.
    • (1993) Models of Hysteresis , pp. 124-142
    • Pokrovskii, A.1
  • 168
    • 65249135785 scopus 로고    scopus 로고
    • Topological degree in locating homoclinic structures for discrete dynamical systems
    • Pokrovskii A., Szybka S.J., Mclnerney J.G. Topological degree in locating homoclinic structures for discrete dynamical systems. Preprints of INS, UCC 2001.
    • (2001) Preprints of INS, UCC
    • Pokrovskii, A.1    Szybka, S.J.2    Mclnerney, J.G.3
  • 169
    • 0039392727 scopus 로고
    • New theorems on forced periodic oscillations and bounded solutions
    • Krasnosel'skii M., Mawhin J., Pokrovskii A. New theorems on forced periodic oscillations and bounded solutions. Soviet Physics Doklady 1991, 36(11):743-745.
    • (1991) Soviet Physics Doklady , vol.36 , Issue.11 , pp. 743-745
    • Krasnosel'skii, M.1    Mawhin, J.2    Pokrovskii, A.3
  • 171
    • 0003492060 scopus 로고
    • Theory of Functional Differential Equations
    • second edition, Springer-Verlag, New York
    • Hale J. Theory of Functional Differential Equations. Applied Mathematical Sciences 1977, vol. 3,. second edition, Springer-Verlag, New York.
    • (1977) Applied Mathematical Sciences
    • Hale, J.1
  • 173
    • 30844453836 scopus 로고    scopus 로고
    • Topological shadowing and split-hyperbolicity
    • (1997)
    • Pokrovskii A. Topological shadowing and split-hyperbolicity. Funct. Differ. Equ. 1998, 4(3-4):335-360. (1997).
    • (1998) Funct. Differ. Equ. , vol.4 , Issue.3-4 , pp. 335-360
    • Pokrovskii, A.1
  • 174
    • 25844499379 scopus 로고    scopus 로고
    • Methods of geometrical analysis of complicated dynamics, with applications to models of semi-conductor lasers
    • Webpage, University College Cork, Cork, Ireland
    • Rasskazov O. Methods of geometrical analysis of complicated dynamics, with applications to models of semi-conductor lasers. PhD thesis 2003, Webpage, University College Cork, Cork, Ireland. http://phys.ucc.ie/~oll/phdthesis.pdf.
    • (2003) PhD thesis
    • Rasskazov, O.1
  • 175
    • 84904240164 scopus 로고    scopus 로고
    • On natural continua of periodic solutions of systems with hysteresis
    • part 1
    • Rachinskii D. On natural continua of periodic solutions of systems with hysteresis. Automat. Remote. Control. 2003, 64(3):420-438. part 1.
    • (2003) Automat. Remote. Control. , vol.64 , Issue.3 , pp. 420-438
    • Rachinskii, D.1
  • 176
    • 84904240216 scopus 로고    scopus 로고
    • On a nonlocal condition for existence of cycles of systems with hysteresis
    • part 1
    • Rachinskii D., Krasnosel'skii A.M. On a nonlocal condition for existence of cycles of systems with hysteresis. Automat. Remote. Control. 2003, 64(2):231-251. part 1.
    • (2003) Automat. Remote. Control. , vol.64 , Issue.2 , pp. 231-251
    • Rachinskii, D.1    Krasnosel'skii, A.M.2
  • 177
    • 0001615349 scopus 로고
    • The method of parameter functionalization in the Hopf bifurcation problem
    • Kozjakin V.S., Krasnosel'skii M.A. The method of parameter functionalization in the Hopf bifurcation problem. Nonlinear Anal. 1987, 11(2):149-161.
    • (1987) Nonlinear Anal. , vol.11 , Issue.2 , pp. 149-161
    • Kozjakin, V.S.1    Krasnosel'skii, M.A.2
  • 178
    • 0003731284 scopus 로고
    • The Hopf Bifurcation and its Applications
    • Springer-Verlag, New York, (With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S
    • Marsden J.E., Mccracken M. The Hopf Bifurcation and its Applications. Applied Mathematical Sciences 1976, vol. 19. Springer-Verlag, New York, (With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S.
    • (1976) Applied Mathematical Sciences , vol.19
    • Marsden, J.E.1    Mccracken, M.2
  • 179
    • 0038394279 scopus 로고
    • Large amplitude cycles in autonomous systems with hysteresis
    • Krasnosel'skii A.M., Krasnosel'skii M.A. Large amplitude cycles in autonomous systems with hysteresis. Dokl. Akad. Nauk SSSR 1985, 283(1):23-26.
    • (1985) Dokl. Akad. Nauk SSSR , vol.283 , Issue.1 , pp. 23-26
    • Krasnosel'skii, A.M.1    Krasnosel'skii, M.A.2
  • 181
    • 0035455420 scopus 로고    scopus 로고
    • On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity
    • Diamond P., Kuznetsov N., Rachinskii D. On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity. J. Differential Equations 2001, 175(1):1-26.
    • (2001) J. Differential Equations , vol.175 , Issue.1 , pp. 1-26
    • Diamond, P.1    Kuznetsov, N.2    Rachinskii, D.3
  • 182
    • 0000100336 scopus 로고
    • Period three implies chaos
    • Li T.Y., Yorke J.A. Period three implies chaos. Amer. Math. Monthly 1975, 82(10):985-992.
    • (1975) Amer. Math. Monthly , vol.82 , Issue.10 , pp. 985-992
    • Li, T.Y.1    Yorke, J.A.2
  • 188
    • 0004009536 scopus 로고
    • Topological Dynamics and Ordinary Differential Equations
    • Van Nostrand Reinhold Co., London
    • Sell G.R. Topological Dynamics and Ordinary Differential Equations. Van Nostrand Reinhold Mathematical Studies, No. 33 1971, Van Nostrand Reinhold Co., London.
    • (1971) Van Nostrand Reinhold Mathematical Studies, No. 33
    • Sell, G.R.1
  • 189
    • 0001788272 scopus 로고
    • Symbolic dynamics II. Sturmian trajectories
    • Morse M., Hedlund G. Symbolic dynamics II. Sturmian trajectories. Amer J. Math. 1940, 62:1-42.
    • (1940) Amer J. Math. , vol.62 , pp. 1-42
    • Morse, M.1    Hedlund, G.2
  • 193
    • 0002326342 scopus 로고
    • Dynamic Bifurcations
    • Springer-Verlag, Berlin, é. Benot (Ed.)
    • Dynamic Bifurcations. Lecture Notes in Mathematics 1991, vol. 1493. Springer-Verlag, Berlin. é. Benot (Ed.).
    • (1991) Lecture Notes in Mathematics , vol.1493
  • 194
    • 0002188388 scopus 로고    scopus 로고
    • Solutions surstables des équations différentielles complexes lentes-rapides à point tournant
    • (6)
    • Benot é., Fruchard A., Schäfke R., Wallet G. Solutions surstables des équations différentielles complexes lentes-rapides à point tournant. Ann. Fac. Sci. Toulouse Math. 1998, 7(4):627-658. (6).
    • (1998) Ann. Fac. Sci. Toulouse Math. , vol.7 , Issue.4 , pp. 627-658
    • Benot, é.1    Fruchard, A.2    Schäfke, R.3    Wallet, G.4
  • 195
    • 0004123124 scopus 로고
    • Universitext, Springer-Verlag, Berlin, F. Diener, M. Diener (Eds.)
    • Nonstandard Analysis in Practice 1995, Universitext, Springer-Verlag, Berlin. F. Diener, M. Diener (Eds.).
    • (1995) Nonstandard Analysis in Practice
  • 198
    • 34250909760 scopus 로고
    • über die magnetische nachwirkung
    • Preisach P. über die magnetische nachwirkung. Zeitschrift für Physik 1938, 94:277-302.
    • (1938) Zeitschrift für Physik , vol.94 , pp. 277-302
    • Preisach, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.