Kopel系统的分岔研究

Study of Bifurcation in Kopel System

应用中心流形定理和分岔理论,证明Kopel系统会发生跨临界分岔和叉式分岔。运用数值方法证明了当临界平衡点失稳时,系统中Neimark-Sacker分岔的存在,即从平衡点处会分岔出稳定的极限环。应用Matlab进行了数值模拟,数值模拟的结果与理论分析一致,而且数值分析展示了更为丰富的动力行为。

With the center manifold theorem and the bifurcation theory, it is proved that transctitical bifurcation and pitchfork bifurcation can appear in Kopel system. The critical equilibrium loses its stability as Neimark- Sacker bifurcation occurs, which is proved by using the numerical method. Matlab is applied to make numerical simulation, the results of which not only show the consistence with the theoretical analysis but also display richer dynamics of the system.