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To realize the synchronization of nonlinear dynamical system, the general control method is unidirectional linear coupling. Research on function coupling of chaos synchronization is not enough, so there arises a question: for nonlinear dynamical system, if chaos synchronization is realized by linear coupling, whether can any type of function coupling always make the system go to chaos synchronization? In this paper, a class of nonlinear dynamical system is considered and the relation between linear coupling and function coupling is investigated. It is proved that if linear coupling can make chaos synchronization, then any function satisfying some conditions can do so too. The condition is given and proved. Finally for Duffing system, three coupling functions are used to prove the analytical result. The simulation results show that the conclusion is correct.
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Keywords:
- function coupling /
- chaos synchronization /
- dynamics
[1] Pecora L M Carroll T L 1990 Phy Rev Lett. 64 821
[2] Han Q, Li C, Huang T 2009 Chaos 19 023105
[3] Monetti R, Bunk W, Aschenbrenner T 2009 Phys. Rev. E 79 046207
[4] Ge Z, Yang C 2008 Chaos 18 043129
[5] Zhou P, Cheng X, Zhang N 2008 Acta Phys. Sin. 57 5407 (in Chinese) [周 平, 程雪峰, 张年英 2008 57 5407]
[6] Yu H, Zheng N 2008 Acta Phys. Sin. 57 4712 (in Chinese) [于洪洁, 郑宁 2008 57 4712]
[7] Yu H, Peng J 2006 Chin. J. comput. Phys. 23 626 (in Chinese) [于洪洁, 彭建华 2006 计算物理 23 626]
[8] Jing X, Lü L 2009 Acta Phys. Sin. 58 7539 (in Chinese) [敬晓丹, 吕翎 2009 58 7539]
[9] Liu B, Peng J 2004 Nonlinear Dynamics (Beijing: High Education Press) (in Chinese) [刘秉正, 彭建华 2004 非线性动力学 (北京: 高等教育出版社)]
[10] Wu X, Cai J, Wang M 2008 Chaos, Soliton. Fract. 36 121
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[1] Pecora L M Carroll T L 1990 Phy Rev Lett. 64 821
[2] Han Q, Li C, Huang T 2009 Chaos 19 023105
[3] Monetti R, Bunk W, Aschenbrenner T 2009 Phys. Rev. E 79 046207
[4] Ge Z, Yang C 2008 Chaos 18 043129
[5] Zhou P, Cheng X, Zhang N 2008 Acta Phys. Sin. 57 5407 (in Chinese) [周 平, 程雪峰, 张年英 2008 57 5407]
[6] Yu H, Zheng N 2008 Acta Phys. Sin. 57 4712 (in Chinese) [于洪洁, 郑宁 2008 57 4712]
[7] Yu H, Peng J 2006 Chin. J. comput. Phys. 23 626 (in Chinese) [于洪洁, 彭建华 2006 计算物理 23 626]
[8] Jing X, Lü L 2009 Acta Phys. Sin. 58 7539 (in Chinese) [敬晓丹, 吕翎 2009 58 7539]
[9] Liu B, Peng J 2004 Nonlinear Dynamics (Beijing: High Education Press) (in Chinese) [刘秉正, 彭建华 2004 非线性动力学 (北京: 高等教育出版社)]
[10] Wu X, Cai J, Wang M 2008 Chaos, Soliton. Fract. 36 121
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