一类超混沌系统的动力学研究及其仿真  

Dynamical analysis of hyper-chaotic system and its simulation

作　　者：张勇[1] 张付臣[2] 张光云[3] 袁红[4] 

机构地区：[1]河南工业职业技术学院,河南南阳473009 [2]重庆大学数学与统计学院,重庆401331 [3]西南石油大学外国语学院,成都610500 [4]临沂大学理学院,山东临沂276005

出　　处：《计算机工程与应用》2014年第22期79-82,共4页Computer Engineering and Applications

基　　金：重庆市自然科学基金（No.2009BB3185）.

摘　　要：混沌系统的全局：憎数吸引集在混沌系统的控制与同步之中起着非常重要的作用。借助一个适当的Lyapunov函数和一元函数极值理论研究了一个新超混沌系统的全局指数吸引集，得到了该系统的全局指数吸引集表达式Q。可以断定在全局指数吸引集Q之外混沌系统的平衡位置、周期解、概周期解、游荡回复解和其他任何混沌吸引子都不复存在，这大大简化了对该系统的分析工作。确定轨线从吸引集外走向吸引集的速度是指数速率。同时得到的全局指数吸引集表远式Q为该系统的控制和同步提供了理论依据。通过计算机进行了模拟，数值模拟与理论计算的结果相吻合。Globally expommtially attractive set of a chaotic system plays an important role in chaos control and chaos syn- chronization. In this paper, the globally exponentially attractive set of a new hyper-chaotic system is studied via constructing a Lyapunov function and tiae function extreme value theory. It has been obtained that the globally exponentially attractive set D for this system. It can be concluded that the system cannot have equilibrium points, periodic solutions, quasiperiodic solutions, or other chaotic attractors outside the globally attractive set t2. This simplifies the analysis of the properties of the hyper-chaotic system. Furthermore, it can be concluded that the rate of the ffajectories of system going from the exterior of the set O to the interior of the set 1＂2 is an exponential rate. The globally exponentially attractive set ~ also provides the theoretic foundation for the chaotic control and chaotic synchronization of the system. Numerical simulations are pre- sented to show the effectiveness of the proposed scheme. Numerical simulation is consistent with the results of theoretical calculation.

关 键 词：超混沌系统 全局指数吸引集 数值仿真 李雅普诺夫函数 

分 类 号：O241.84[理学—计算数学] O29[理学—数学]