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Volumn 61, Issue 3, 2010, Pages 407-417

A new chaotic system with fractional order and its projective synchronization

Author keywords

Chaos; Fractional order system; New chaotic system; Projective synchronization; Rikitake system

Indexed keywords

CHAOS; FRACTIONAL-ORDER SYSTEMS; NEW CHAOTIC SYSTEM; PROJECTIVE SYNCHRONIZATION; RIKITAKE SYSTEM;

EID: 77956595176     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9658-x     Document Type: Article
Times cited : (56)

References (42)
  • 1
    • 0000241853 scopus 로고
    • Deterministic non-periodic flow
    • Lorenz, E. N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130-141 (1963)
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 3
    • 0034738985 scopus 로고    scopus 로고
    • The Lorenz attractor exists
    • Stewart, I.: The Lorenz attractor exists. Nature 406, 948-949 (2002)
    • (2002) Nature , vol.406 , pp. 948-949
    • Stewart, I.1
  • 4
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rössler, O. E.: An equation for continuous chaos. Phys. Lett. A 57, 397-398 (1976)
    • (1976) Phys. Lett. A , vol.57 , pp. 397-398
    • Rössler, O.E.1
  • 5
    • 33751555569 scopus 로고
    • Some simple chaotic flows
    • Sprott, J. C.: Some simple chaotic flows. Phys. Rev. E 50, R647 (1994)
    • (1994) Phys. Rev. E , vol.50
    • Sprott, J.C.1
  • 6
    • 62249200922 scopus 로고    scopus 로고
    • Yet another chaotic attractor
    • Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9, 1465-1466 (1999)
    • (1999) Int. J. Bifurc. Chaos , vol.9 , pp. 1465-1466
    • Chen, G.1    Ueta, T.2
  • 7
    • 0036011505 scopus 로고    scopus 로고
    • A new chaotic attractor coined
    • Lü, J. H., Chen, G. R.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 3, 659-661 (2002)
    • (2002) Int. J. Bifurc. Chaos , vol.3 , pp. 659-661
    • Lü, J.H.1    Chen, G.R.2
  • 10
    • 33748691599 scopus 로고    scopus 로고
    • A new modified hyperchaotic Lü system
    • Wang, G., Zhang, X., Zheng, Y., Li, X.: A new modified hyperchaotic Lü system. Physica A 371, 260-272 (2006)
    • (2006) Physica A , vol.371 , pp. 260-272
    • Wang, G.1    Zhang, X.2    Zheng, Y.3    Li, X.4
  • 12
    • 84968498322 scopus 로고
    • Oscillations of a system of disk dynamos
    • Rikitake, T.: Oscillations of a system of disk dynamos. Proc. Camb. Philos. Soc. 54, 89-95 (1958)
    • (1958) Proc. Camb. Philos. Soc. , vol.54 , pp. 89-95
    • Rikitake, T.1
  • 13
    • 0019145350 scopus 로고
    • Chaos in the Rikitake two-disk dynamo system
    • Keisuke, I.: Chaos in the Rikitake two-disk dynamo system. Earth Planet. Sci. Lett. 51, 451-457 (1980)
    • (1980) Earth Planet. Sci. Lett. , vol.51 , pp. 451-457
    • Keisuke, I.1
  • 16
    • 0021440218 scopus 로고
    • Application of fractional calculus to the theory of viscoelasticity
    • Koeller, R. C.: Application of fractional calculus to the theory of viscoelasticity. J. Appl. Mech. 51, 299-307 (1984)
    • (1984) J. Appl. Mech. , vol.51 , pp. 299-307
    • Koeller, R.C.1
  • 17
    • 0021424253 scopus 로고
    • Linear approximation of transfer function with a pole of fractional order
    • Sun, H. H., Abdelwahad, A. A., Onaral, B.: Linear approximation of transfer function with a pole of fractional order. IEEE Trans. Automat. Control 29, 441-444 (1984)
    • (1984) IEEE Trans. Automat. Control , vol.29 , pp. 441-444
    • Sun, H.H.1    Abdelwahad, A.A.2    Onaral, B.3
  • 18
    • 0010178279 scopus 로고
    • An analog simulation of noninteger order transfer functions for analysis of electrode process
    • Ichise, M., Nagayanagi, Y., Kojima, T.: An analog simulation of noninteger order transfer functions for analysis of electrode process. J. Electroanal. Chem. 33, 253-265 (1971)
    • (1971) J. Electroanal. Chem. , vol.33 , pp. 253-265
    • Ichise, M.1    Nagayanagi, Y.2    Kojima, T.3
  • 21
    • 3342927052 scopus 로고    scopus 로고
    • Chaos and hyperchaos in the fractionalorder Rössler equations
    • Li, C. G., Chen, G.: Chaos and hyperchaos in the fractionalorder Rössler equations. Physica A 341, 55-61 (2004)
    • (2004) Physica A , vol.341 , pp. 55-61
    • Li, C.G.1    Chen, G.2
  • 22
    • 1842832060 scopus 로고    scopus 로고
    • Chaos in Chen's system with a fractional order
    • Li, C. P., Peng, G. J.: Chaos in Chen's system with a fractional order. Chaos Solitons Fractals 22, 443-450 (2004)
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 443-450
    • Li, C.P.1    Peng, G.J.2
  • 23
    • 18844427587 scopus 로고    scopus 로고
    • Chaos synchronization of the fractional Lü system
    • Deng, W., Li, C. P.: Chaos synchronization of the fractional Lü system. Physica A 353, 61-72 (2005)
    • (2005) Physica A , vol.353 , pp. 61-72
    • Deng, W.1    Li, C.P.2
  • 24
    • 0343689904 scopus 로고
    • Synchronization in chaotic systems
    • Pecora, L. M., Carroll, T. L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824 (1990)
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 821-824
    • Pecora, L.M.1    Carroll, T.L.2
  • 25
    • 33846354268 scopus 로고    scopus 로고
    • Modified projective synchronization of chaotic system
    • Li, G. H.: Modified projective synchronization of chaotic system. Chaos Solitons Fractals 32, 1786-1790 (2007)
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 1786-1790
    • Li, G.H.1
  • 26
    • 34548535118 scopus 로고    scopus 로고
    • Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input
    • Hung, M. L., Yan, J. J., Liao, T. L.: Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input. Chaos Solitons Fractals 35, 181-187 (2008)
    • (2008) Chaos Solitons Fractals , vol.35 , pp. 181-187
    • Hung, M.L.1    Yan, J.J.2    Liao, T.L.3
  • 27
    • 1442354755 scopus 로고    scopus 로고
    • Synchronization of fractional order chaotic systems
    • Li, C. G., Liao, X. F., Yu, J. B.: Synchronization of fractional order chaotic systems. Phys. Rev. E 68, 067203 (2003)
    • (2003) Phys. Rev. E , vol.68 , pp. 067203
    • Li, C.G.1    Liao, X.F.2    Yu, J.B.3
  • 28
    • 19144371559 scopus 로고    scopus 로고
    • Chaotic dynamics and synchronization of fractional-order Arneodo's systems
    • Lu, J. G.: Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos Solitons Fractals 26, 1125-1133 (2005)
    • (2005) Chaos Solitons Fractals , vol.26 , pp. 1125-1133
    • Lu, J.G.1
  • 29
    • 33749553588 scopus 로고    scopus 로고
    • The synchronization of three fractional differential systems
    • DOI 10.1016/j.chaos.2005.11.020, PII S0960077905011100
    • Li, C., Yan, J.: The synchronization of three fractional differential systems. Chaos Solitons Fractals 32, 751-757 (2007) (Pubitemid 44537765)
    • (2007) Chaos, Solitons and Fractals , vol.32 , Issue.2 , pp. 751-757
    • Li, C.1    Yan, J.2
  • 30
    • 35748971445 scopus 로고    scopus 로고
    • Synchronization of chaotic fractional-order systems via active sliding mode controller
    • Tavazoei, M. S., Haeri, M.: Synchronization of chaotic fractional-order systems via active sliding mode controller. Physica A 387, 57-70 (2008)
    • (2008) Physica A , vol.387 , pp. 57-70
    • Tavazoei, M.S.1    Haeri, M.2
  • 31
    • 0033240334 scopus 로고    scopus 로고
    • The Rikitake two-disk dynamo system and domains with periodic orbits
    • Hardy, Y., Steeb, W. H.: The Rikitake two-disk dynamo system and domains with periodic orbits. Int. J. Theor. Phys. 38, 2413-2417 (1999)
    • (1999) Int. J. Theor. Phys. , vol.38 , pp. 2413-2417
    • Hardy, Y.1    Steeb, W.H.2
  • 33
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent
    • Caputo, M.: Linear models of dissipation whose Q is almost frequency independent. Geophys. J. R. Astron. Soc. 13, 529-539 (1967)
    • (1967) Geophys. J. R. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 37
    • 0037332868 scopus 로고    scopus 로고
    • Chaos in fractional-order autonomous nonlinear systems
    • Ahmad, W. M., Sprott, J. C.: Chaos in fractional-order autonomous nonlinear systems. Chaos Solitons Fractals 16, 339-351 (2003)
    • (2003) Chaos Solitons Fractals , vol.16 , pp. 339-351
    • Ahmad, W.M.1    Sprott, J.C.2
  • 38
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • Diethelm, K.: An algorithm for the numerical solution of differential equations of fractional order. Electron. Trans. Numer. Anal. 5, 1-6 (1997) (Pubitemid 38870919)
    • (1997) Electronic Transactions on Numerical Analysis , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 39
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Diethelm, K., Ford, N. J., Freed, A. D.: A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29, 3-22 (2002)
    • (2002) Nonlinear Dyn , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 40
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • Diethelm, K., Ford, N. J.: Analysis of fractional differential equations. J. Math. Anal. Appl. 265, 229-248 (2002)
    • (2002) J. Math. Anal. Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 41
    • 4043121080 scopus 로고    scopus 로고
    • Detailed error analysis for a fractional Adams method
    • Diethelm, K., Ford, N. J., Freed, A. D.: Detailed error analysis for a fractional Adams method. Numer. Algorithms 36, 31-52 (2004)
    • (2004) Numer. Algorithms , vol.36 , pp. 31-52
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.