Newmark方法求解二阶常微分方程Hopf分支等价性

发布时间：2018-05-31 05:22

本文选题：二阶微分方程 + Hopf分支　；参考：《黑龙江大学自然科学学报》2017年01期

【摘要】：考虑一个带有参数的二阶常微分系统,对其线性化方程的特征方程根进行分析,研究系统平衡点的稳定性,得到系统产生Hopf分支的充分条件。利用Newmark方法将系统离散,分析离散系统特征方程根的分布情况,确定方法中的参数,保证对任意的步长离散系统存在Neimark-Sacker分支。证明在离散系统Neimark-Sacker分支存在的情况下,原连续系统具有Hopf分支。数值仿真验证了结果的有效性和适用性。
[Abstract]:In this paper, we consider a second order ordinary differential system with parameters, analyze the root of the characteristic equation of its linearized equation, study the stability of the equilibrium point of the system, and obtain the sufficient conditions for the system to produce Hopf bifurcation. The Newmark method is used to discretize the system. The distribution of the root of the characteristic equation of the discrete system is analyzed and the parameters in the method are determined to guarantee the existence of Neimark-Sacker bifurcation for any step discrete system. It is proved that the original continuous system has Hopf bifurcation in the case of the existence of Neimark-Sacker bifurcation for discrete systems. The validity and applicability of the results are verified by numerical simulation.
【作者单位】：哈尔滨工业大学(威海)理学院;
【基金】：国家自然科学基金资助项目(11301115;11271101)
【分类号】：O175

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