Concurrent homoclinic bifurcation and Hopf bifurcation for a class of planar Filippov systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Li, Liping¹  Huang, Lihong^2,3 

[1] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Zhejiang, Peoples R China

[2] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[3] Hunan Womens Univ, Changsha 410004, Hunan, Peoples R China

关键词: Planar Filippov systems;    Homoclinic bifurcation;    Hopf bifurcation;    Limit cycle;   

DOI  :  10.1016/j.jmaa.2013.09.025

来源: Elsevier

【 摘 要 】

This paper investigates both homoclinic bifurcation and Hopf bifurcation which occur concurrently in a class of planar perturbed discontinuous systems of Filippov type. Firstly, based on a geometrical interpretation and a new analysis of the so-called successive function, sufficient conditions are proposed for the existence and stability of homoclinic orbit of unperturbed systems. Then, with the discussion about Poincare map, bifurcation analyses of homoclinic orbit and parabolic parabolic (PP) type pseudo-focus are presented. It is shown that two limit cycles can appear from the two different kinds of bifurcation in planar Filippov systems. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free