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Volumn 71, Issue 1-2, 2013, Pages 241-257

Chaos in the fractional-order complex Lorenz system and its synchronization

Author keywords

Dynamic property; Fractional order complex Lorenz system; Synchronization

Indexed keywords

CHAOTIC SYSTEMS; LYAPUNOV METHODS;

EID: 84867977717     PISSN: 0924090X     EISSN: 1573269X     Source Type: Journal    
DOI: 10.1007/s11071-012-0656-z     Document Type: Article
Times cited : (141)

References (33)
  • 1
    • 33645304553 scopus 로고    scopus 로고
    • Modeling and control of dynamic systems using fractional calculus: Application to electrochemical processes and flexible structures
    • Vinagre, B.M., Feliu, V.: Modeling and control of dynamic systems using fractional calculus: application to electrochemical processes and flexible structures. In: Proceedings of 41st IEEE Conference on Decision and Control, Las Vegas, pp. 214-239 (2002)
    • (2002) Proceedings of 41St IEEE Conference on Decision and Control, Las Vegas , pp. 214-239
    • Vinagre, B.M.1    Feliu, V.2
  • 5
    • 84866136226 scopus 로고    scopus 로고
    • Nonlinear state-observer control for projective synchronization of a fractional-order hyperchaotic system
    • Liu, L., Liang, D.L., Liu, C.X.: Nonlinear state-observer control for projective synchronization of a fractional-order hyperchaotic system. Nonlinear Dyn. 69(4), 1929-1939 (2012)
    • (2012) Nonlinear Dyn , vol.69 , Issue.4 , pp. 1929-1939
    • Liu, L.1    Liang, D.L.2    Liu, C.X.3
  • 8
    • 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
  • 9
    • 2042470796 scopus 로고    scopus 로고
    • Chaos in the fractional order Chen system and its control
    • Li, C.G., Chen, G.R.: Chaos in the fractional order Chen system and its control. Chaos Solitons Fractals 22, 549-554 (2004)
    • (2004) Chaos Solitons Fractals , vol.22 , pp. 549-554
    • Li, C.G.1    Chen, G.R.2
  • 11
    • 77954194607 scopus 로고    scopus 로고
    • Bifurcations and chaos in fractional-order simplified Lorenz system
    • Sun, K.H., Wang, X., Sprott, J.C.: Bifurcations and chaos in fractional-order simplified Lorenz system. Int. J. Bifurc. Chaos 4, 1209-1219 (2010)
    • (2010) Int. J. Bifurc. Chaos , vol.4 , pp. 1209-1219
    • Sun, K.H.1    Wang, X.2    Sprott, J.C.3
  • 12
    • 0000367731 scopus 로고
    • Single-modelaser phase dynamics. Phys
    • Roldan, E., Devalcarcel, G.J., Vilaseca, R.: Single-modelaser phase dynamics. Phys. Rev. A 48(1), 591-598 (1993)
    • (1993) Rev. A , vol.48 , Issue.1 , pp. 591-598
    • Roldan, E.1    Devalcarcel, G.J.2    Vilaseca, R.3
  • 13
    • 0013044957 scopus 로고
    • Detuned lasers and the complex Lorenz equations-subcritical and supercritical Hopf bifurcations
    • Ning, C.Z., Haken, H.: Detuned lasers and the complex Lorenz equations-subcritical and supercritical Hopf bifurcations. Phys. Rev. A 41(7), 3826-3837 (1990)
    • (1990) Phys. Rev. A , vol.41 , Issue.7 , pp. 3826-3837
    • Ning, C.Z.1    Haken, H.2
  • 14
    • 0000288953 scopus 로고    scopus 로고
    • Boundedness of attractors in the complex Lorenz model
    • Toronov, V.Y., Derbov, V.L.: Boundedness of attractors in the complex Lorenz model. Phys. Rev. E 55(3), 3689-3692 (1997)
    • (1997) Phys. Rev. E , vol.55 , Issue.3 , pp. 3689-3692
    • Toronov, V.Y.1    Derbov, V.L.2
  • 15
    • 73949132376 scopus 로고    scopus 로고
    • Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay
    • Zhang, H.G., Liu, Z.W., Huang, G.B., Wang, Z.S.: Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans. Neural Netw. 21(1), 91-106 (2010)
    • (2010) IEEE Trans. Neural Netw , vol.21 , Issue.1 , pp. 91-106
    • Zhang, H.G.1    Liu, Z.W.2    Huang, G.B.3    Wang, Z.S.4
  • 16
    • 78049473650 scopus 로고    scopus 로고
    • Complete synchronization of chaotic complex nonlinear systems with uncertain parameters
    • Mahmoud, G.M., Mahmoud, E.E.: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters. Nonlinear Dyn. 62(4), 875-882 (2010)
    • (2010) Nonlinear Dyn , vol.62 , Issue.4 , pp. 875-882
    • Mahmoud, G.M.1    Mahmoud, E.E.2
  • 17
    • 34250733018 scopus 로고    scopus 로고
    • Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems
    • Liu, Y.J., Wang, W.: Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems. Inf. Sci. 177(18), 3901-3917 (2007)
    • (2007) Inf. Sci , vol.177 , Issue.18 , pp. 3901-3917
    • Liu, Y.J.1    Wang, W.2
  • 18
    • 84863983340 scopus 로고    scopus 로고
    • Complex projective synchronization in coupled chaotic complex dynamical systems
    • Wu, Z.Y., Duan, J.Q., Fu, X.C.: Complex projective synchronization in coupled chaotic complex dynamical systems. Nonlinear Dyn. 69(3), 771-779 (2012)
    • (2012) Nonlinear Dyn , vol.69 , Issue.3 , pp. 771-779
    • Wu, Z.Y.1    Duan, J.Q.2    Fu, X.C.3
  • 19
    • 68249152437 scopus 로고    scopus 로고
    • Adaptive robust fuzzy control for a class of uncertain chaotic systems
    • Liu, Y.J., Zheng, Y.Q.: Adaptive robust fuzzy control for a class of uncertain chaotic systems. Nonlinear Dyn. 57(3), 431-439 (2009)
    • (2009) Nonlinear Dyn , vol.57 , Issue.3 , pp. 431-439
    • Liu, Y.J.1    Zheng, Y.Q.2
  • 20
    • 79960150696 scopus 로고    scopus 로고
    • Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems
    • Liu, Y.J., Chen, C.L.P., Wen, G.X., Tong, S.C.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22(7), 1162-1167 (2011)
    • (2011) IEEE Trans. Neural Netw , vol.22 , Issue.7 , pp. 1162-1167
    • Liu, Y.J.1    Chen, C.L.P.2    Wen, G.X.3    Tong, S.C.4
  • 21
    • 77952582245 scopus 로고    scopus 로고
    • Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control
    • Zhang, H.G., Ma, T.D., Huang, G.B., Wang, Z.L.: Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(3), 831-844 (2010)
    • (2010) IEEE Trans. Syst. Man Cybern., Part B, Cybern , vol.40 , Issue.3 , pp. 831-844
    • Zhang, H.G.1    Ma, T.D.2    Huang, G.B.3    Wang, Z.L.4
  • 22
    • 72949089051 scopus 로고    scopus 로고
    • Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters
    • Liu, Y.J., Wang, W., Tong, S.C., Liu, Y.S.: Robust adaptive tracking control for nonlinear systems based on bounds of fuzzy approximation parameters. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 40(1), 170-184 (2010)
    • (2010) IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum , vol.40 , Issue.1 , pp. 170-184
    • Liu, Y.J.1    Wang, W.2    Tong, S.C.3    Liu, Y.S.4
  • 27
    • 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
  • 28
    • 78149315322 scopus 로고    scopus 로고
    • Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional
    • Liu, Z.W., Zhang, H.G., Zhang, Q.L.: Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional. IEEE Trans. Neural Netw. 21(11), 1710-1718 (2010)
    • (2010) IEEE Trans. Neural Netw , vol.21 , Issue.11 , pp. 1710-1718
    • Liu, Z.W.1    Zhang, H.G.2    Zhang, Q.L.3
  • 30
    • 72149089014 scopus 로고    scopus 로고
    • Chaos control of a fractional order modified coupled dynamos system
    • Wang, X.Y., He, Y.J. Wang, M.J.: Chaos control of a fractional order modified coupled dynamos system. Nonlinear Anal. 71, 6126-6134 (2009)
    • (2009) Nonlinear Anal , vol.71 , pp. 6126-6134
    • Wang, X.Y.1    He, Y.J.2    Wang, M.J.3
  • 32
    • 0021224909 scopus 로고
    • Determining Lyapunov exponents from a time series
    • Wolf, A., Swinney, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285-317 (1985)
    • (1985) Physica D , vol.16 , pp. 285-317
    • Wolf, A.1    Swinney, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 33
    • 43949166788 scopus 로고
    • A practical method for calculating largest Lyapunov exponents from small data sets
    • Rosenstein, M.T., Collins, J.J., De, L.C.J.: A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117-134 (1993)
    • (1993) Physica D , vol.65 , pp. 117-134
    • Rosenstein, M.T.1    Collins, J.J.2    De, L.C.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.