【摘要】 通过弱非线性非自治系统的VanderPol变换下的平均化方程与Poincar啨映射的关系 ,导出了一个混沌存在的必要条件 ,作为混沌预测的一个重要判据 ;并以VanderPol_Duffing方程作为实例 ,与Mel’nikov方法和文献 [2 ]提出的方法得出的结果进行比较 .结果表明 ,本文提出的方法优于上述两种方法 .更多还原

【Abstract】 By studying the relation between the averaging equation under Van der Pol transformation and the Poincaré map for weak_nonlinear two_order dynamical systems, an essential condition which provides an important criteria for chaos is presented. To examine its reliability, we provide an example, which illustrates this criteria superior to Mel’nikov method and the method given in ref.. The results show that the method presented by us outmatches aforesaid methods.更多还原