分段线性混沌系统周期轨道稳定性分析

A new method of stability analysis for periodic orbits of piecewise linear chaotic systems

提出对分段线性混沌系统周期轨道进行稳定性分析和判断的新方法.利用庞加莱映射将周期轨道的稳定性分析转化为映射平面上不动点的稳定性分析.基于分段线性混沌系统周期轨道的解析解,导出周期轨道的庞加莱映射方程及其雅可比矩阵,根据雅可比矩阵的特征值和特征向量的分析可确定周期轨道的稳定性、吸引方向及排斥方向.以蔡氏电路为例,用该方法分析了许多周期轨道的稳定性,并通过数字仿真对所有分析结果进行验证,结果表明该方法正确且实用.

This paper proposed a new method of stability analysis for periodic orbits of piecewise linear chaotic systems. With the help of Poincare mapping, the stability problem of periodic orbits was changed to that of the fixed points on the mapping plane. The Poincare Mapping equation and the Jacobian Matrix of periodic orbits could be deduced from the time domain solutions of periodic orbits of piecewise linear chaotic system. Based on the eigenvalues and eigenvectors of the Jacobian Matrix, the stability of periodic orbits and the attracting and repelling directions of the trajectory could be determined. As examples, the stability of many periodic orbits of Chau＇s circuits was analyzed and determined by this new method. All the results are exactly the same as that of digital simulation, which shows that the new method is correct and practical.