一类具有忆阻器的Lorenz型混沌系统余维二分岔及无穷远处动力学分析  

Codimension-2 Bifurcation Dynamics and Infinity Analysis of a Class of Lorenz Chaos Systems With Memristors

作　　者：黄俊 陈玉明 HUANG Jun;CHEN Yuming(School of Mathematics and Systems Science,Guangdong Polytechnic Normal University,Guangzhou 510665,P.R.China)

机构地区：[1]广东技术师范大学数学与系统科学学院,广州510665

出　　处：《应用数学和力学》2020年第11期1275-1283,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11701104);广东省普通高校特色创新项目(2016KTSCX076)。

摘　　要：基于经典的Lorenz系统,通过反馈控制的方式得到了一类具有忆阻器的三维混沌系统,对该系统分别从局部高余维分岔及无穷远全局动力学行为这两个方面进行了研究.首先,基于平均理论,对原点平衡点处的zero-Hopf分岔行为进行了分析;其次,基于中心流形理论,对原点平衡点处的double-zero分岔进行了分析;最后,根据Poincaré紧致化方法,对该系统在无穷远处的动力学行为进行了研究.Based on the classical Lorenz system,a class of 3D memristive chaotic systems were obtained through feedback control,and the local high codimensional bifurcation and the infinite global dynamic behavior of the system were studied.Firstly,according to the average theory,the zero-Hopf bifurcation behavior at the origin equilibrium point was analyzed.Secondly,with the center manifold theory,the double-zero bifurcation at the origin of the system was investigated.Finally,according to the Poincarécompactification method,the dynamics at infinity of the system was discussed.

关 键 词：LORENZ系统 zero-Hopf分岔 double-zero分岔 无穷远动力学 

分 类 号：O175[理学—数学]