应用同伦分析法研究Mathieu-Duffing振子的周期解

Period solutions of Mathieu-Duffing oscillator by the homotopy analysis method

应用同伦分析法研究了Mathieu-Duffing振子的周期解,展示了Mathieu-Duffing振子的周期1和周期2解的求解过程,通过求解构造的非线性代数方程组而获得周期解,应用Floquet理论判别了周期解的稳定性。比较了同伦分析方法得到的周期解和数值方法得到的周期解,结果表明两者具有一致性。

In this paper,the period motion of the Mathieu-Duffing oscillator is investigated by the homo-topy analysis method. The procedures of the solution of the period-1 and period-2 are presented. The period solutions are obtained by solving the nonlinear algebraic equations. Stability of the period motion is judged by the Floquet theory. The phase portraits of period solution obtained by the homotopy analysis method agree well with those obtained by the numerical time-integration method.