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Coexistence of anti-phase and complete synchronization in the generalized Lorenz system. (English) Zbl 1222.93126
Summary: We investigate a class of new synchronization phenomena. Some control strategy is established to guarantee the coexistence of anti-phase and complete synchronization in the generalized Lorenz system. The efficiency of the control scheme is revealed by some illustrative simulations.
MSC:
93C40Adaptive control systems
37D45Strange attractors, chaotic dynamics
34H10Chaos control (ODE)
34D06Synchronization
References:
[1]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic system, Phys rev lett 64, 821-824 (1990)
[2]Rodriguez, E.; George, N.: Perceptions shadow: long-distance synchronization of human brain activity, Nature (London) 397, 430-443 (1999)
[3]Robert, C. E.; Selverston, A. I.: Synchronous behavior of two coupled biological neurons, Phys rev E 81, 5692-5695 (1998)
[4]Grzybowski, J. M. V.; Rafikov, M.; Balthazar, J. M.: Synchronization of the unified chaotic system and application in secure communication, Commun nonlinear sci numer simul 14, 2793-2806 (2009) · Zbl 1221.94047 · doi:10.1016/j.cnsns.2008.09.028
[5]Luo, A. C. J.: A theory for synchronization of dynamical systems, Commun nonlinear sci numer simul 14, 1901-1951 (2009) · Zbl 1221.37218 · doi:10.1016/j.cnsns.2008.07.002
[6]Liu, W.; Qian, X.; Yang, J.; Xiao, J.: Anti-synchronization in coupled chaotic oscillators, Phys lett A 354, 119-125 (2006)
[7]Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J.: Phase synchronization of chaotic oscillators, Phys rev lett 76, 1804-1807 (1996)
[8]Hu, M. F.; Xu, Z. Y.; Zhang, R.: Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems, Commun nonlinear sci numer simul 13, No. 2, 456-464 (2008) · Zbl 1123.37013 · doi:10.1016/j.cnsns.2006.05.003
[9]Chen, G. R.; Dong, X. M.: From chaos to order: perspectives, methodologies and application, (1999)
[10]Bowong, S.: Adaptive synchronization between two different chaotic dynamical systems, Commun nonlinear sci numer simul 12, 976-985 (2007) · Zbl 1115.37030 · doi:10.1016/j.cnsns.2005.10.003
[11]Rafikov, M.; Balthazar, J.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Commun nonlinear sci numer simul 13, 1246-1255 (2008) · Zbl 1221.93230 · doi:10.1016/j.cnsns.2006.12.011
[12]Lorenz, E. N.: Deterministic nonperiodic flow, J atmos sci 20, 130-141 (1963)
[13]Lü, J.; Chen, G.; Cheng, D.; Celikovsky, S.: Bridge the gap between the Lorenz system and the Chen system, Int J bifurcat chaos 12, 2917-2926 (2002) · Zbl 1043.37026 · doi:10.1142/S021812740200631X
[14]Huang, C. F.; Cheng, K. H.; Yan, J. J.: Robust chaos synchronization of four-dimensional energy resource systems subject to unmatched uncertainties, Commun nonlinear sci numer simul 14, No. 6, 2784-2792 (2009)
[15]Celikovsky, S.; Chen, G.: On the generalized Lorenz canonical form, Chaos, solitons fractals 26, 1271-1276 (2005) · Zbl 1100.37016 · doi:10.1016/j.chaos.2005.02.040
[16]Barblart, I.: Systems dèquations differentielled òscillations nonlinearies, Rev roumaine math pures appl 4, 267-270 (1959)