一类简单二次非线性Sprott混沌系统的分析与控制  

Analysis and Control of a Class of Sprott Chaotic System with Simple Quadratic Nonlinearities

作　　者：付景超[1] 孙敬[1] 李鹏松[1] 

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《吉林大学学报（理学版）》2015年第3期395-400,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金青年基金(批准号:11201057);吉林省自然科学基金(批准号:20130101065JC);吉林省教育厅"十二五"科学技术研究项目(批准号:2013429)

摘　　要：用自适应反推方法考虑一类简单非线性Sprott混沌系统的控制问题,得到了平衡点的稳定性及Hopf分岔存在性的条件,通过Lyapunov指数图及混沌吸引子验证了系统的混沌现象,通过分岔图分析得到了系统存在复杂动力学行为,并设计自适应反推控制器控制混沌系统到给定的平衡点.数值仿真验证了所设计控制器的有效性.The control problems of a class of nonlinear Sprott simple chaotic systems were solved via an adaptive backstepping method. Firstly, the conditions of stability of the equilibria point and the existence of Hopf bifurcation were obtained. Secondly., chaotic phenomenon of the system was verified by means of presenting Lyapunov exponent and chaotic attractor, and complex dynamic behaviors were found via analyzing bifurcation diagram. Finally, an adaptive backstepping controller was designed to control chaotic system to a given equilibrium point. Numerical simulation has shown the effectiveness of the controller designed.

关 键 词：Sprott混沌系统 LYAPUNOV指数 分岔 自适应反推 

分 类 号：O231.2[理学—运筹学与控制论]