Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation

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• 作者：Fengjie Geng (1) gengfengjie_hbu@163.com
  Yancong Xu (23) yancongx@163.com
• 关键词：Local coordinate moving frame &#8211 ; Pitchfork bifurcation &#8211 ; Generic heteroclinic loop &#8211 ; Nonhyperbolic equilibrium
• 刊名：Nonlinear Dynamics
• 出版年：2012
• 出版时间：October 2012
• 年：2012
• 卷：70
• 期：2
• 页码：1645-1655
• 全文大小：571.6 KB
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• 作者单位：1. College of Mathematics and Science, China University of Geosciences (Beijing), Beijing, 100083 China2. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036 China3. Division of Applied Mathematics, Brown University, Providence, 02912 USA
• ISSN：1573-269X

文摘

In this paper, using the local coordinate moving frame approach, we investigate bifurcations of generic heteroclinic loop with a hyperbolic equilibrium and a nonhyperbolic equilibrium which undergoes a pitchfork bifurcation. Under some generic hypotheses, the existence of homoclinic loop, heteroclinic loop, periodic orbit and three or four heteroclinic orbits is obtained. In addition, the non-coexistence conditions for homoclinic loop and periodic orbit are also given. Note that the results achieved here can be extended to higher dimensional systems.