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In this paper, a new three-dimensional autonomous chaotic system is constructed by adding a product term with variable coefficient to the first equation of Chen's system. The new system with different groups of coefficients can be chaotic or not by adjusting the variable coefficient, that is, by adjusting the variable coefficient, chaos occurs in new system when Chen's system is not chaotic, or chaos is suppressed in new system even if Chen's system is chaotic. The characteristics of the new chaotic system are analyzed in detail and the synchronization of new system is considered. Moreover, the simulation results are also presented.
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Keywords:
- Chen's system /
- the new three-dimensional autonomous chaotic system /
- chaos suppression /
- synchronization
[1] Liu B Z, Peng J H 2007 Nonlinear Dynamics (Beijing: Higher Education Press) pp120--131 (in Chinese) [刘秉正, 彭建华 2007 非线性动力学 (北京: 高等教育出版社) 第120---131页]
[2] [3] Chen G R, L J H 2003 Dynamic Analysis, Control and Synchronization of Lorenz System Families (Beijing: Science Press) pp9--130 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、 控制与同步 (北京: 科学出版社) 第9---130页]
[4] [5] Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[6] L J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[7] [8] L J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[9] [10] [11] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[12] [13] Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍, 齐国元, 陈增强, 张宇辉, 袁著祉 2006 物理学报 55 4005]
[14] [15] Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[16] Tomasz K (translated by Shi Y) 2008 Chaos for Engineers: Theory, Application, and Control (2nd Ed.) ( Beijing: National Defense Industry Press) p62 (in Chinese) [卡毕坦尼亚克著 (施引译) 2008 面向工程的混沌学-----理论、 应用及控制(第2版) (北京: 国防工业出版社) 第62页]
[17] [18] [19] Zhong G Q, Tang W K S 2002 Int. J. Bifur. Chaos 12 1423
[20] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[21] -
[1] Liu B Z, Peng J H 2007 Nonlinear Dynamics (Beijing: Higher Education Press) pp120--131 (in Chinese) [刘秉正, 彭建华 2007 非线性动力学 (北京: 高等教育出版社) 第120---131页]
[2] [3] Chen G R, L J H 2003 Dynamic Analysis, Control and Synchronization of Lorenz System Families (Beijing: Science Press) pp9--130 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、 控制与同步 (北京: 科学出版社) 第9---130页]
[4] [5] Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[6] L J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[7] [8] L J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[9] [10] [11] Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[12] [13] Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍, 齐国元, 陈增强, 张宇辉, 袁著祉 2006 物理学报 55 4005]
[14] [15] Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[16] Tomasz K (translated by Shi Y) 2008 Chaos for Engineers: Theory, Application, and Control (2nd Ed.) ( Beijing: National Defense Industry Press) p62 (in Chinese) [卡毕坦尼亚克著 (施引译) 2008 面向工程的混沌学-----理论、 应用及控制(第2版) (北京: 国防工业出版社) 第62页]
[17] [18] [19] Zhong G Q, Tang W K S 2002 Int. J. Bifur. Chaos 12 1423
[20] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[21]
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