【摘要】 应用摄动 增量法研究一类平面多项式微分方程的极限环相图 ,半稳定极限环分叉和极限环个数的计算问题 .该方法的特点是用有限Fourier级数给出极限环的近似解析表达式 ,把微分方程化为线性增量方程 ,应用谐波平衡法建立Fourier系数的线性代数方程组 ,再用迭代法求解 .二次系统的算例表明该方法是有效的更多还原

【Abstract】 The limit cycle phase portraits, the semi stable limit cycle bifurcation and the number of limit cycles for certain planar polynomial differential equations are studied by using the perturbation incremental method. The essence of this method is to construct an approximate analytical expression in terms of Fourier series for the limit cycle. Firstly, the governing differential equations are transformed into linearized incremental equations. Then a set of linearized algebraic equations in terms of Fourier coefficients is set up. Finally, the linear equations are solved iteratively. A quadratic system is taken as an example to show the efficiency and the accuracy of the present method.更多还原