NIU Ben, GUO Yu-xiao, SUN Wei. Global Existence of Homoclinic Orbits in a Class of Neutral Equations[J]. 2014, 19(2): 95-100.DOI: 10.15938/j.jhust.2014.02.002.
一类中立型方程的全局同宿轨分支
摘要
研究中立型微分差分方程的余维二分支有助于揭示此类系统的复杂动力学行为.给出推导中立型微分差分方程余维二分支规范型的中心流形约化方法:首先介绍中立型微分差分方程相空间的分解方法;其次给出中立型微分差分方程约化在中心流形上规范型的计算方法;最后推导了一类具有扩展时滞控制的van de Pol方程的BT分支规范型
进而得到了平衡点附近的大范围存在的同宿轨分支线
同时给出了数值结果. 更多还原
Abstract
Investigating codimension two bifurcations in neutral differential-difference equations may reveal thecomplicated dynamics. In this paper,center manifold reduction method is established to derive the normal formsnear the codimension two bifurcations in NDDE. We first introduce the decomposition of the phase space of NDDE.Then the normal form method to reduce a NDDE onto an invariant center manifold is obtained. Finally,BT bifurca-tion in van de Pol's equation with extended delay feedback is considered and the detailed dynamics,including theglobally existed homoclinic orbits,are obtained near the equilibrium.