基于Lorenz系统的强迫Lorenz混沌系统的动力学研究  

Dynamical behavior for the forced Lorenz system based on the Lorenz map and simulation

作　　者：尹社会[1] 张勇[1] 张付臣[2] 张光云[3] 

机构地区：[1]河南工业职业技术学院,河南南阳473000 [2]重庆工商大学数学与统计学院,重庆400067 [3]西南石油大学外国语学院,四川成都610500

出　　处：《东北师大学报（自然科学版）》2014年第1期42-47,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：重庆市自然科学基金资助项目(2009BB3185);中央高校基本科研业务费(CDJXS10100029;CDJXS11100026);南阳市科技发展计划项目(2012GG035;2013GG048);南阳市科技发展计划项目(2013RK013)

摘　　要：通过给出了强迫Lorenz混沌系统的动力系统模型,借助一簇广义正定、径向无界的Lyapunov函数和最优化理论研究了混沌系统的正半轨线的有界性,得到了正半轨线界估计的表达式,数值模拟表明了方案的可行性.The boundedness of a chaotic system is important in chaos control, synchronization and other applications. The boundedness of the forced Lorenz system is investigated via constructing a family of Lyapunov functions and optimation theory. The globally exponentially attractive set and positive invariant set are obtained for this system. Furthermore, we can conclude that the rate of the trajectories of the system going from the exterior of the setΩλ to the interior of the set Ωλ is an exponential rate. The estimate of the trajectories rate is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme.

关 键 词：LORENZ系统 有界性 数值仿真 

分 类 号：O175.8[理学—数学]