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Impulsive synchronization for a chaotic system with channel time-delay. (English) Zbl 1221.37214
Summary: This paper discusses the synchronization of the chaotic system. Some new and less conservative sufficient conditions are established by impulsive control method with channel time-delay and different time-varying parameter uncertainties. An example and its simulations are finally included to visualize the effectiveness and feasibility of the method.
MSC:
37N35Dynamical systems in control
37D45Strange attractors, chaotic dynamics
34D06Synchronization
34A37Differential equations with impulses
References:
[1]Lorenz, E. N.: Deterministic nonperiodic flow, J atmos sci 20, 130 (1963)
[2]Chen, G.; Ueta, T.: Yet another chaotic attractor, Int J bifurcat chaos 9, 1465 (1999) · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[3]Matsumoto, T.; Chua, L. O.; Kobayashi, K.: Hyperchaos: laboratory experiment and numerical confirmation, IEEE trans circuits syst 33, 1143 (1986)
[4]Li, Y.; Tang, S. K.; Chen, G.: Generating hyperchaos via state feedback control, Int J bifurcat chaos 15, No. 10, 3367 (2005)
[5]Yan, Z.: Controlling hyperchaos in the new hyperchaotic Chen system, Appl math comput 168, 1239 (2005) · Zbl 1160.93384 · doi:10.1016/j.amc.2004.10.016
[6]Ott, E.; Grebogi, C.; Yorke, J. A.: Controlling chaos, Phys rev lett 64, 1196 (1990) · Zbl 0964.37501 · doi:10.1103/PhysRevLett.64.1196
[7]Pecora, L.; Carroll, T.: Synchronization in chaotic systems, Phys rev lett 64, 821 (1990) · Zbl 0938.37019
[8]Wu, X.; Lu, J.: Parameter identification and backstepping control of uncertain L system, Chaos solitons fractals 18, 721 (2003) · Zbl 1068.93019 · doi:10.1016/S0960-0779(02)00659-8
[9]Wu, X.; Lu, J.: Adaptive control of uncertain L system, Chaos solitons fractals 22, 375 (2004) · Zbl 1062.93516 · doi:10.1016/j.chaos.2004.02.012
[10]Lu, J.; Zhou, T.; Zhang, S.: Chaos synchronization between linearly coupled chaotic systems, Chaos solitons fractals 14, 529 (2002) · Zbl 1067.37043 · doi:10.1016/S0960-0779(02)00005-X
[11]Guan, Z.: Decentralized stabilization for impulsive large scale systems with delays, Dynam continuous discrete impuls syst 6, 369 (1999) · Zbl 0934.93009
[12]Lu, J.; Wu, X.; Lii, J.: Synchronization of a unified chaotic system and the application in secure communication, Phys lett A 305, 365 (2002) · Zbl 1005.37012 · doi:10.1016/S0375-9601(02)01497-4
[13]Brown, R.; Kocarev, L.: A unified definition of synchronization for dynamical systems, Chaos 10, 344-349 (2000) · Zbl 0973.34041 · doi:10.1063/1.166500
[14]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys rev lett 64, 821-824 (1990)
[15]Chen, M. Y.; Han, Z. Z.: Controlling and synchronizing chaotic Genesio system via nonlinear feedback control, Chaos solitons fractals 17, 709-716 (2003) · Zbl 1044.93026 · doi:10.1016/S0960-0779(02)00487-3
[16]Huang, H.; Li, H. X.; Zhong, J.: Master-slave synchronization of general Lur’e systems with time-varying delay and parameter uncertainty, Int J bifurcat chaos 16, 281-294 (2006) · Zbl 1097.94004 · doi:10.1142/S0218127406014800
[17]Zhang, H.; Ma, X. K.; Liu, W. Z.: Synchronization of chaotic systems with parametric uncertainty using active sliding mode control, Chaos solitons fractals 21, 1249-1257 (2004) · Zbl 1061.93514 · doi:10.1016/j.chaos.2003.12.073
[18]Xia, Y.; Yang, Z.; Han, M.: Lag synchronization of unknown chaotic delayed yangcyang-type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification, IEEE trans neural networks 20, No. 7, 1165-1180 (2009)
[19]Xia, Y.; Yang, Z.; Han, M.: Synchronization schemes for coupled identical yangcyang type fuzzy cellular neural networks, Commun nonlinear sci numer simulat 14, 3645-3659 (2009) · Zbl 1221.37227 · doi:10.1016/j.cnsns.2009.01.028
[20]Ding, W.; Han, M.: Synchronization of delayed fuzzy cellular neural networks based on adaptive control, Phys lett A 372, 4674-4681 (2008) · Zbl 1221.94094 · doi:10.1016/j.physleta.2008.04.053
[21]Zhang, H. G.; Xie, Y. H.; Wang, Z. L.; Zhen, C. D.: Adaptive synchronization between two different chaotic neural networks with time delay, IEEE trans neural networks 18, 1841-1845 (2007)
[22]Chen, D. L.; Sun, J. T.; Huang, C. S.: Impulsive control and synchronization of general chaotic system, Chaos solitons fractals 28, 213-218 (2006) · Zbl 1091.93023 · doi:10.1016/j.chaos.2005.05.057
[23]Zhang, H.; Ma, X. K.: Synchronization of uncertain chaotic systems with parametric perturbation via active control, Chaos solitons fractals 21, 39-47 (2004) · Zbl 1048.37031 · doi:10.1016/j.chaos.2003.09.014
[24]Yuxia, L.; Wallace, K.; Chen, G.: Generating hyperchaos via state feedback control, Int J bifurcat chaos 15, 3367-3375 (2005)
[25]Al-Sawalha, M. Mossa; Noorani, M. S. M.: Anti-synchronization of two hyperchaotic systems via nonlinear control, Commun nonlinear sci numer simulat 14, No. 8, 3402-3411 (2009) · Zbl 1221.37210 · doi:10.1016/j.cnsns.2008.12.021
[26]Jiang, G. P.; Zheng, W. X.; Chen, G. R.: Global chaos synchronization with channel time-delay, Chaos solitons fractals 20, 267-275 (2004) · Zbl 1045.34021 · doi:10.1016/S0960-0779(03)00374-6