Codimension-3 bifurcations of a class of homoclinic loop with saddle-point

✍ Scribed by Guifeng Deng; Deming Zhu

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 853 KB
• Volume: 69
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.10.013

✦ Synopsis

In this work, bifurcations in the class that the homoclinic orbit connects the strong stable and strong unstable manifolds of a saddle are investigated for four-dimensional vector fields. The existence, numbers, coexistence and incoexistence of 1-homoclinic orbit, 1-periodic orbit, 2 n -homoclinic orbit and 2 n -periodic orbit are obtained, the approximate expressions of the corresponding bifurcation surfaces and the bifurcation diagrams are also presented.