一类三次Lie'nard系统的稳定性与Hopf分支分析

Stability and Hopf Bifurcation Analysis for a Class of Cubic Lie'nard Systems

研究了一类三次Lie'nard系统当其参数发生微小改变时系统相图的基本结构变化情况.应用Hopf分支理论进行包括分支方向、轨道稳定性等分析,得出了系统在参数取某特定值时会发生Hopf分支,并运用Matlab软件进行数值模拟验证了所得结论的正确性.

A class of cubic liefiard systems that contains parameters was studied The basic structure of the systems will change when the parameter values change slightly. With Hopf bifurcation theory, the bifurcation direction and track stability of the systems were analyzed. The results show that Hopf bifurcation occurs when the parameters of the systems are specified as certain fixed values. Numerical simulation with Matlab proves that the obtained conclusion is correct.