一类Van der Pol-Duffing振子的隐藏吸引子

Hidden Attractors of a Class of Van der Pol-Duffing Oscillator

【目的】分析和研究Van der Pol-Duffing系统中的隐藏吸引子问题。【方法】根据Routh-Hurwitz判据,运用经典动力系统Hopf分支理论,利用谐波线性化方法和分析-数值方法,研究该系统中平衡点的稳定性以及隐藏吸引子的存在性。【结果】该系统存在隐藏吸引子,并且会出现隐藏吸引子分别与稳定的平衡点、稳定的周期轨、混沌吸引子共存的现象。【结论】该系统具有更为复杂的动力学行为,包括周期轨、混沌吸引子与隐藏吸引子。

[Purposes]In order to analyze and study the problem of hidden attractors in Van der Pol-Duffing system,some new research results are obtained.[Methods]According to the Routh-Hurwitz criterion,using the Hopf bifurcation theory of the classical dynamic system,the harmonic linearization method and the analytical-numerical method are used to study the stability of the equilibrium points and the existence of hidden attractors in the system.[Findings]There are hidden attractors in the system,and there are phenomena in which hidden attractors coexist with stable equilibrium points,stable periodic orbits,and chaotic attractors.[Conclusions]It is concluded that the system has more complex dynamic behaviors,including periodic orbits,chaotic attractors and hidden attractors.