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Volumn 9, Issue 1-2, 1998, Pages 1-18

Bifurcations for Heteroclinic Orbits of a Periodic Motion and a Saddle-focus and Dynamical Chaos

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; NONLINEAR EQUATIONS; ORBITS; SET THEORY;

EID: 0031653886     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(97)00044-1     Document Type: Article
Times cited : (5)

References (28)
  • 1
    • 0000675441 scopus 로고
    • On the appearance and structure of Lorenz attractor
    • Afraimovich, V. S., Bykov, V. V. and Shil'nikov, L. P., On the appearance and structure of Lorenz attractor. DAN SSSR, 1977, 234, 336-339.
    • (1977) DAN SSSR , vol.234 , pp. 336-339
    • Afraimovich, V.S.1    Bykov, V.V.2    Shil'nikov, L.P.3
  • 2
    • 0000119416 scopus 로고
    • On the structurally unstable attracting limit sets of Lorenz attractor type
    • Afraimovich, V. S., Bykov, V. V. and Shil'nikov, L. P., On the structurally unstable attracting limit sets of Lorenz attractor type. Tran. Mosc. Soc., 1983, 2, 153-215.
    • (1983) Tran. Mosc. Soc. , vol.2 , pp. 153-215
    • Afraimovich, V.S.1    Bykov, V.V.2    Shil'nikov, L.P.3
  • 3
    • 0002768228 scopus 로고
    • Strange attractors and quasi-attractors
    • eds G. I. Barenblatt, G. Iooss and D. D. Joseph. Pitman, NY
    • Afraimovich, V. S. and Shil'nikov, L. P., Strange attractors and quasi-attractors. In Nonlinear Dynamics and Turbulence, eds G. I. Barenblatt, G. Iooss and D. D. Joseph. Pitman, NY, 1983, pp. 1-28.
    • (1983) Nonlinear Dynamics and Turbulence , pp. 1-28
    • Afraimovich, V.S.1    Shil'nikov, L.P.2
  • 4
    • 0001852216 scopus 로고
    • Invariant two-dimensional tori, their breakdown and stochastisity
    • Gorky University Press
    • Afraimovich, V. S., Shil'nikov, L. P., Invariant two-dimensional tori, their breakdown and stochastisity. In Methods of Qualitative Theory of Differential Equations. Gorky University Press, 1983 (transl. Am. Math. Soc. Trans., 1991, 149(2), 201-212).
    • (1983) Methods of Qualitative Theory of Differential Equations
    • Afraimovich, V.S.1    Shil'nikov, L.P.2
  • 5
    • 0000697407 scopus 로고
    • Afraimovich, V. S., Shil'nikov, L. P., Invariant two-dimensional tori, their breakdown and stochastisity. In Methods of Qualitative Theory of Differential Equations. Gorky University Press, 1983 (transl. Am. Math. Soc. Trans., 1991, 149(2), 201-212).
    • (1991) Am. Math. Soc. Trans. , vol.149 , Issue.2 , pp. 201-212
  • 6
    • 0041192420 scopus 로고
    • The theory of bifurcations and turbulence 1
    • Shil'nikov, L. P., The theory of bifurcations and turbulence 1. Select. Math. Sov., 1991, 101, 43-53.
    • (1991) Select. Math. Sov. , vol.101 , pp. 43-53
    • Shil'nikov, L.P.1
  • 8
    • 0002635901 scopus 로고
    • Birth and death of the double-scroll
    • Matsumoto, T., Chua, L. O. and Komuro, M., Birth and death of the double-scroll. Physica D, 1987, 24, 97-124.
    • (1987) Physica D , vol.24 , pp. 97-124
    • Matsumoto, T.1    Chua, L.O.2    Komuro, M.3
  • 9
    • 0026153216 scopus 로고
    • Intermittency in piecewise-linear circuit
    • Chua, L. O., Lin, G., Intermittency in piecewise-linear circuit. IEE Trans. Circuits and Systems, 1991, 38(5), 510-520.
    • (1991) IEE Trans. Circuits and Systems , vol.38 , Issue.5 , pp. 510-520
    • Chua, L.O.1    Lin, G.2
  • 10
    • 0040005100 scopus 로고
    • Bifurcations in a piecewise linear system
    • George, D. P., Bifurcations in a piecewise linear system. Phys. Lett. A, 1986, 1181, 17-21.
    • (1986) Phys. Lett. A , vol.1181 , pp. 17-21
    • George, D.P.1
  • 11
    • 2742611797 scopus 로고
    • A case study for homoclinic chaos in an autonomous electronic circuit
    • Freire, E., Rodriquez-Luis, A. J., Gamero, E. and Ponce, E., A case study for homoclinic chaos in an autonomous electronic circuit. Physica D, 1993, 62, 230-253.
    • (1993) Physica D , vol.62 , pp. 230-253
    • Freire, E.1    Rodriquez-Luis, A.J.2    Gamero, E.3    Ponce, E.4
  • 12
    • 0002995706 scopus 로고
    • A contribution to the problem of a rough equilibrium state of saddle-focus type
    • Shil'nikov, L. P., A contribution to the problem of a rough equilibrium state of saddle-focus type. Math. USSR Sbornik, 1970, 10, 92-103.
    • (1970) Math. USSR Sbornik , vol.10 , pp. 92-103
    • Shil'nikov, L.P.1
  • 13
    • 79955579216 scopus 로고
    • On systems with a saddle-focus homoclinic curve
    • Ovsyannikov, I. M. and Shil'nikov, L. P., On systems with a saddle-focus homoclinic curve. Math. USSR Sbornik, 1987, 58, 91-102.
    • (1987) Math. USSR Sbornik , vol.58 , pp. 91-102
    • Ovsyannikov, I.M.1    Shil'nikov, L.P.2
  • 14
    • 0000936965 scopus 로고
    • On three-dimensional systems close to systems with a structurally unstable homoclinic curve
    • Gavrilov, N. K. and Shilnikov, L. P., On three-dimensional systems close to systems with a structurally unstable homoclinic curve. Math. USSR Sbornik, 1973, 17, 446-485.
    • (1973) Math. USSR Sbornik , vol.17 , pp. 446-485
    • Gavrilov, N.K.1    Shilnikov, L.P.2
  • 15
    • 51249181043 scopus 로고
    • The abundance of wild hyperbolic sets and non-smooth stable sets for diffeormorphism
    • Newhouse, S. E., The abundance of wild hyperbolic sets and non-smooth stable sets for diffeormorphism. Publ. Math. IHES, 1979, 50, 101-151.
    • (1979) Publ. Math. IHES , vol.50 , pp. 101-151
    • Newhouse, S.E.1
  • 16
    • 4244116032 scopus 로고
    • Chua's circuit: Rigorous results and future problems
    • Shil'nikov, L. P., Chua's circuit: rigorous results and future problems. Int. J. Bifurcation and Chaos, 43, 1994, 489-519.
    • (1994) Int. J. Bifurcation and Chaos , vol.43 , pp. 489-519
    • Shil'nikov, L.P.1
  • 17
    • 0000234956 scopus 로고
    • Versal unfolding of equivariant vector fields for the cases of the symmetry of the second and third orders
    • Transl. I. G. Petrovsky, In Russian
    • Harozov, E. I., Versal unfolding of equivariant vector fields for the cases of the symmetry of the second and third orders (Transl. I. G. Petrovsky, Seminar, 1979, Vol. 5, pp. 163-192. In Russian).
    • (1979) Seminar , vol.5 , pp. 163-192
    • Harozov, E.I.1
  • 19
    • 0040598359 scopus 로고
    • Bifurcation of systems with homoclinic curve of saddle-focus
    • Belyakov, L. A., Bifurcation of systems with homoclinic curve of saddle-focus. Math. Notes Acad. Sci. USSR, 1984, 36, 838-843.
    • (1984) Math. Notes Acad. Sci. USSR , vol.36 , pp. 838-843
    • Belyakov, L.A.1
  • 20
    • 0039341143 scopus 로고
    • Bifurcation phenomena in the 1:1 resonant horn for the forced van der Pol-Duffing equations
    • Dmitriev, A. S., Komlev, Yu. A., Turaev, D. V., Bifurcation phenomena in the 1:1 resonant horn for the forced van der Pol-Duffing equations. Int. J. Bifurcation and Chaos, 1992, 2(1), 93-100.
    • (1992) Int. J. Bifurcation and Chaos , vol.2 , Issue.1 , pp. 93-100
    • Dmitriev, A.S.1    Komlev, Yu.A.2    Turaev, D.V.3
  • 21
    • 0013534692 scopus 로고
    • Confinor and bounded-time patterns in Chua's circuit and the double-scroll family
    • Lozi, R. and Ushiki, S., Confinor and bounded-time patterns in Chua's circuit and the double-scroll family. Int. J. Bifurcation and Chaos, 1991, 11, 119-138.
    • (1991) Int. J. Bifurcation and Chaos , vol.11 , pp. 119-138
    • Lozi, R.1    Ushiki, S.2
  • 22
    • 21344482326 scopus 로고
    • The theory of confinors in Chua's circuit: Accurate analysis of bifurcations and attractors
    • Lozi, R. and Ushiki, S., The theory of confinors in Chua's circuit: accurate analysis of bifurcations and attractors. Int. J. Bifurcation and Chaos, 1993, 32, 333-361.
    • (1993) Int. J. Bifurcation and Chaos , vol.32 , pp. 333-361
    • Lozi, R.1    Ushiki, S.2
  • 24
    • 0000949321 scopus 로고
    • New type of strange attractor from a geometric model of Chua's circuit
    • Belykh, V. N. and Chua, L. O., New type of strange attractor from a geometric model of Chua's circuit. Int. J. Bifurcation and Chaos, 1992, 2(3), 697-704.
    • (1992) Int. J. Bifurcation and Chaos , vol.2 , Issue.3 , pp. 697-704
    • Belykh, V.N.1    Chua, L.O.2
  • 25
    • 0039233435 scopus 로고
    • On existence of a smooth invariant foliation for maps of Lorenz type
    • In Russian
    • Shashkov, M. V. and Shil'nikov, L. P., On existence of a smooth invariant foliation for maps of Lorenz type. Differenzial'nye uravnenija, 1994, 304, 586-595In Russian.
    • (1994) Differenzial'nye Uravnenija , vol.304 , pp. 586-595
    • Shashkov, M.V.1    Shil'nikov, L.P.2
  • 27
    • 0000063614 scopus 로고
    • On a Poincaré-Birkgoff problem
    • Shil'nikov, L. P., On a Poincaré-Birkgoff problem. Math. USSR Sbornik, 1968, 3, 353-371.
    • (1968) Math. USSR Sbornik , vol.3 , pp. 353-371
    • Shil'nikov, L.P.1
  • 28
    • 0010149727 scopus 로고
    • Homoclinic orbits in a parametrized saddle-focus system
    • Feroe, J. A., Homoclinic orbits in a parametrized saddle-focus system. Physica D, 1993, 621-4, 254-262.
    • (1993) Physica D , vol.621 , Issue.4 , pp. 254-262
    • Feroe, J.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.