Inverse Jacobian multipliers and Hopf bifurcation on center manifolds

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Zhang, Xiang^1,2 

[1] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China

关键词: Inverse Jacobian multiplier;    Hopf bifurcation;    Normal form;    Center;    Focus;   

DOI  :  10.1016/j.jde.2014.02.002

来源: Elsevier

【 摘 要 】

In this paper we consider a class of higher dimensional differential systems in R-n which have a two dimensional center manifold at the origin with a pair of pure imaginary eigenvalues. First we characterize the existence of either analytic or C-infinity inverse Jacobian multipliers of the systems around the origin, which is either a center or a focus on the center manifold. Later we study the cyclicity of the system at the origin through Hopf bifurcation by using the vanishing multiplicity of the inverse Jacobian multiplier. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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