Affiliation:
1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, P. R. China
Abstract
We have studied a Filippov system [Formula: see text] with small [Formula: see text], [Formula: see text] and [Formula: see text] being periodic. Since [Formula: see text] is an abstract function, the subharmonic Melnikov function cannot be computed. In other words, for this system the Melnikov method loses effectiveness. First, we proved that the equation has a unique harmonic solution, a unique [Formula: see text]-subharmonic solution for any [Formula: see text] and they are Lyapunov asymptotically stable. Moreover, this equation has no other type of periodic solutions. Further, the attractor of this system is not chaotic. Finally, some numerical examples are given.
Funder
National Natural Science Foundation of China
Cultivation Foundation of Excellent Doctoral Dissertation of Southwest Jiaotong University
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)
Cited by
2 articles.
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