Melnikov method for homoclinic bifurcation in nonlinear impact oscillators

✍ Scribed by Zhengdong Du; Weinian Zhang

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 746 KB
• Volume: 50
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2005.03.007

✦ Synopsis

Based on an mverted pendulum impacting on rigid walls under external periodm excitation, a class of nonhnear impact oscillators is discussed for its homochnic bifurcation The Melmkov method established for smooth dynamical systems is extended to be applicable to the nonsmooth one For nonlinear Impact systems, closed form solutions between impacts are generally unavailable. The absence of closed form solutions makes difficulties in estimation of the gap between the stable manifold and unstable manifold In this paper, we give a method to compute the Melnikov functions up to the nth-order so as to obtain conditions of parameters for the persistence of homochmc cycles whmh are formed via the identification given by the impact rule.