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Comparison of feedback control methods for a hyperchaotic Lorenz system. (English) Zbl 1235.93111
Summary: More and more attention has been payed to the hyperchaotic system for the huge potential applications of hyperchaotic system such as secure communication and more complex structure than chaotic system. So at present the controlling of the hyperchaotic system simply and effectively is a frontier topic of nonlinear science. In this Letter, for the latest hyperchaotic Lorenz system, four feedback control methods were studied with analytic solution and necessary numerical simulations. It is found that the enhancing feedback control approach is the best choice of the given four feedback control methods for its relatively simple external inputs and relatively small necessary feedback coefficient after comparison. The conclusion is a helpful for the choice of control methods of any other chaotic and hyperchaotic systems.
MSC:
93B52Feedback control
34H10Chaos control (ODE)
34C28Complex behavior, chaotic systems (ODE)
34A34Nonlinear ODE and systems, general
94A60Cryptography
References:
[1]Lorenz, E. N.: J. at. Sci., J. at. Sci. 20, 130 (1963)
[2]Ott, E.; Grebogi, C.; Yorke, J. A.: Phys. rev. Lett., Phys. rev. Lett. 64, 1196 (1990)
[3]Chen, G. R.; Dong, X.: From chaos to order: methodologies, perspectives and applications, (1998)
[4]Wang, Xingyuan; Wang, Mingjun: Physica A, Physica A 387, 3751 (2008)
[5]Yan, Zhenya; Yu, Pei: Chaos solitons fractals, Chaos solitons fractals 35, 333 (2008)
[6]Yan, Zhenya: Appl. math. Comput., Appl. math. Comput. 168, 1239 (2005)
[7]Dou, Fuquan: Commun. nonlinear sci. Numer. simul., Commun. nonlinear sci. Numer. simul. 14, 552 (2009)
[8]Tao, Chaohai: Chaos solitons fractals, Chaos solitons fractals 23, 259 (2005)
[9]Tao, Chaohai; Liu, Xuefei: Chaos solitons fractals, Chaos solitons fractals 32, 1572 (2007)
[10]Tao, Chaohai: Phys. lett. A, Phys. lett. A 348, 201 (2006)
[11]Yang, Qigui: Nonlinear anal.: real world appl., Nonlinear anal.: real world appl. 10, 1601 (2009)
[12]Jia, Qiang: Phys. lett. A, Phys. lett. A 366, 217 (2007)
[13]Chen, Zengqiang: Phys. lett. A, Phys. lett. A 360, 696 (2007)