一类非线性系统的混沌特征分析

Chaotic characteristics analysis of a nonlinear system

提出了一类新的三维非线性自治动力系统.根据稳定性理论分析了系统的定性行为,然后通过计算系统的Lyapunov指数和Lyapunov维数,讨论了系统随参数变化的动力学行为.结果表明,随着参数的变化,系统可能是周期的、拟周期的和混沌的.通过绘制系统的分岔图、相图和Poincare截面图等证实了结果.

A new three-dimensional nonlinear autonomous system is presented,and the qualitative behaviors of the system are analyzed according to the stability theories.By calculating the Lyapunov exponents and the Lyapunov dimensions of the system,the dynamical behaviors of the system with evaluating all the parameters are discussed.The results show that with variation of some parameters,the system may be periodic,quasi-periodic and chaotic.And the results are verified by bifurcation diagrams,phase portraits and Poincare maps.