分段线性动态系统周期轨道的时域法求解及其稳定性分析
doi: 10.3724/SP.J.1146.2006.00902
A New Method of Time Domain Solution and Stability Analysis for Periodic Orbits of Piecewise Linear Dynamic Systems
-
摘要: 该文提出了分段线性动态系统周期轨道的时域法求解及稳定性判断的新方法。分段线性动态系统的状态空间被切换面分割成若干个线性子区间。借助MATLAB,联合求解周期轨道在各子区间的状态转移方程,可得该周期轨道在各切换面的切换点坐标及在各子区间的运行时间,从而得到该周期轨道的分段时间表达式。由该表达式,可导出该周期轨道在某一切换面的庞加莱映射方程及其雅可比矩阵,根据其特征值可判断周期轨道的稳定性。以三阶、四阶蔡氏电路为例,用该方法求出了它们的多个周期轨道,进行了稳定性判断,数字仿真表明该文所提出的新方法是可行的和正确的。Abstract: This paper proposes a new method to get time solutions of periodic orbits and to determine their stability for piecewise linear dynamic systems. The state space of piecewise linear dynamic system is cut into some linear subspaces by several switching surfaces. By solving together all the equations of periodic orbit in these subspaces with MATLAB, the coordinates of periodic orbit on each switching surface and the running time on each subspace are obtained, from which the time expressions in sections of periodic orbit can be derived. Based on these expressions, the Poincare mapping equation and the Jacobian matrix of periodic orbits can be deduced. According to the eigenvalues of the Jacobian matrix, the stability of the periodic orbit can be determined. Using 3rd-order and 4th-order Chaus circuits as examples, the time expressions of many periodic orbits are obtained and their stability is determined respectively by the new method. The results are exact the same as that of digital simulations, which shows the new method is correct and practical.
-
丘水生. 混沌吸引子周期轨道理论研究(Ⅱ)[J]. 电路与系统学报, 2004, 9(1): 1-5.Qiu Shui-sheng. Study on periodic orbit theory of chaoticattractors (Ⅱ) [J]. Journal of Circuits and Systems, 2004,9(1): 1-5.[2]Qiu Shui-Sheng. Calculation of steady-state oscillations innon-linear circuits[J].Int. J. Electronics.1989, 67(3):403-414[3]丘水生. 非线性网络与系统[M]. 成都: 电子科技大学出版社,1990, 第8 章-第10 章.[4]Qiu Shui-Sheng. On verification of limit cycle stability inautonomous nonlinear systems [J].IEEE Trans. on CircuitsSyst.1988, 35(8):1062-1064[5]Silva C. Shilnikov theorem-a tutorial[J].IEEE Trans. onCircuits Syst.-I.1993, 40(10):675-682[6]郝柏林. 从抛物线谈起混沌动力学引论[M]. 上海: 上海科技教育出版社, 1993: 20-24.[7]Matsumoto T, Chua L O, and Kobayashi K. Hyperchaos:Laboratory experiment and numerical confirmation[J]. IEEETrans on circuits Syst., 1986, 33(11): 1143-1147.[8]Auerbach D, Cvitanovic P, and Eckmann J, et al.. Exploringchaotic motion through periodic orbits[J].Phys. Rev. Lett.1987,58(23):2387-2389
计量
- 文章访问数: 3371
- HTML全文浏览量: 88
- PDF下载量: 771
- 被引次数: 0