非线性扰动方程的动力学特性

NON-LINEAR PERTURBED DIFFERENTIAL EQUATIONS DYNAMICAL BEHAVIOURS

用Melnikov函数方法分析了自治扰动系统的奇异轨道在扰动后的稳定流形与不稳定流形的相对位置,给出了系统分支出极限环的条件。描述了自治系统在周期扰动下的紊动性态和次谐轨道。

In this paper,anthor has analysed the relative position between the stable manifold and the unstable manifold of the homochinic oribit of the autonomous system with melnikov function method,getting the conditions which the system bifurcates limit circles. At last, giving the conditions that the system occure Chaos and subharmohic oribits after periodic perturbations.