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In this paper, a new algorithm for all Lyapunov Exponents precisely configuraling a discrete-time dynamical system is proposed. A given deterministic discrete-time dynamical system can be chaotified by the algorithm. A new feed-back controller is designed via moduling operation. All Lyapunov Exponents of the controlled system are equal to a given set of ones. The new controller is simple and can be used to control or anti-control a chaotic system . The corresponding proof as well as two illustrative examples are presented. The simulation results show the effectiveness of the algorithm.
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Keywords:
- discrete-time dynamical system /
- anticontrol of chaos /
- control of chaos /
- Lyapunov exponents placement
[1] Chen G, Lai D 1996 Int. J. of Bifur. Chaos 6 1341
[2] Chen G, Lai D 1997 Proceedings of the 1997 IEEE Conf. Decision and control, SanDiego, CA, Dec 10—12 , 367
[3] Chen G, Lai D 1998 Int. J. of Bifur. Chaos 8 1585
[4] Oseledec V I 1968 Trans. Moscow Math. Soc. 19 197
[5] Devaney R L 1987 An Introduction to Chaotic Dynamical Systems (New York: Addison-Wesley) 10—15
[6] Li T Y, Yorke J A 1975 Amer. Math. Monthly 82 481
[7] Wang X F, Chen G 2000 IEEE Trans. on Cir. Sys. I 47 410
[8] Wang X F, Chen G 2000 J. Control Theory Appl. 17 336
[9] Chen G R, Wang X F 2006 Chaotification of Dynamical Systems—Theory, Method and applications (Shanghai: Shanghai Jiaotong University Press) p18—21 (in Chinese) [陈关荣、 汪 小帆 2006 动力系统的混沌化——理论、 方法与应用 (上海: 上海交通大学出版社) 第18—21页] 〖10] Touhey P 1997 Amer. Math. Monthly 5 411
[10] Chen G R, Wang X F 2006 Chaotification of Dynamical Systems—Theory, Method and applications ( Shanghai: Shanghai Jiaotong University Press) p11—13 (in Chinese) [陈关荣、 汪小帆 2006 动力系统的混沌化——理论、方法与应用(上海:上海交通大学出版社) 第11—13页]
[11] Wen S H 2008 Acta Phys. Sin. 57 5209 (in chinese)[温淑焕 2008 57 5209]
[12] Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 529
[13] Ren H P, Liu D, Han C Z 2006 Acta Phys. Sin. 55 2694 (in chinese)[任海鹏、 刘 丁、 韩崇昭 2006 55 2694]
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[1] Chen G, Lai D 1996 Int. J. of Bifur. Chaos 6 1341
[2] Chen G, Lai D 1997 Proceedings of the 1997 IEEE Conf. Decision and control, SanDiego, CA, Dec 10—12 , 367
[3] Chen G, Lai D 1998 Int. J. of Bifur. Chaos 8 1585
[4] Oseledec V I 1968 Trans. Moscow Math. Soc. 19 197
[5] Devaney R L 1987 An Introduction to Chaotic Dynamical Systems (New York: Addison-Wesley) 10—15
[6] Li T Y, Yorke J A 1975 Amer. Math. Monthly 82 481
[7] Wang X F, Chen G 2000 IEEE Trans. on Cir. Sys. I 47 410
[8] Wang X F, Chen G 2000 J. Control Theory Appl. 17 336
[9] Chen G R, Wang X F 2006 Chaotification of Dynamical Systems—Theory, Method and applications (Shanghai: Shanghai Jiaotong University Press) p18—21 (in Chinese) [陈关荣、 汪 小帆 2006 动力系统的混沌化——理论、 方法与应用 (上海: 上海交通大学出版社) 第18—21页] 〖10] Touhey P 1997 Amer. Math. Monthly 5 411
[10] Chen G R, Wang X F 2006 Chaotification of Dynamical Systems—Theory, Method and applications ( Shanghai: Shanghai Jiaotong University Press) p11—13 (in Chinese) [陈关荣、 汪小帆 2006 动力系统的混沌化——理论、方法与应用(上海:上海交通大学出版社) 第11—13页]
[11] Wen S H 2008 Acta Phys. Sin. 57 5209 (in chinese)[温淑焕 2008 57 5209]
[12] Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 529
[13] Ren H P, Liu D, Han C Z 2006 Acta Phys. Sin. 55 2694 (in chinese)[任海鹏、 刘 丁、 韩崇昭 2006 55 2694]
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