Rssler系统的分岔和混沌的深入探讨

Further study on bifurcation and chaos characters of Rssler system

通过数值研究和仿真,分析了Rssler方程在不同相空间上的吸引子特性,利用分岔图和Lyapunov指数谱分析了分岔参数变化时系统的复杂非线性动力学行为。通过局部放大的分岔图验证了系统由倍周期分岔通向混沌的过程,揭示了系统内禀的复杂性;通过选取不同的庞加莱截面,验证了系统的混沌运动和吸引子的特性。

The character and stability of the chaotic attractor of Roessler system in different phase spaces were analyzed. The complex nonlinear behavior was concentrated on by bifurcation diagrams and Lyapunov exponents with the change of bifurcation parameter. And the route from periodic-doubling to chaos was demonstrated by local enlarged bifurcation diagrams. The chaotic dynamical behaviors and chaotic attractors were validated on different Poincare maps.