一类中立型方程的全局同宿轨分支  

Global Existence of Homoclinic Orbits in a Class of Neutral Equations

作　　者：牛犇[1] 郭宇潇[2] 孙伟[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080 [2]哈尔滨工业大学数学系,黑龙江哈尔滨150001

出　　处：《哈尔滨理工大学学报》2014年第2期95-100,共6页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金资助项目(11301117);黑龙江省教育厅科学技术研究项目(12531136)

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.Investigating codimension two bifurcations in neutral differential-difference equations may reveal the complicated dynamics.In this paper,center manifold reduction method is established to derive the normal forms near 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 bifurcation in van de Pol＇s equation with extended delay feedback is considered and the detailed dynamics,including the globally existed homoclinic orbits,are obtained near the equilibrium.

关 键 词：分支 时滞 高余维 中立型 同宿轨分支 

分 类 号：O175.15[理学—数学]