BIFURCATION OF LIMIT CYCLES IN SMALL PERTURBATIONS OF A CLASS OF HYPER-ELLIPTIC HAMILTONIAN SYSTEMS OF DEGREE 5 WITH A CUSP | Zendy

Ali Atabaigi | Zendy; Hamid R. Z. Zangeneh | Zendy

Open Access

BIFURCATION OF LIMIT CYCLES IN SMALL PERTURBATIONS OF A CLASS OF HYPER-ELLIPTIC HAMILTONIAN SYSTEMS OF DEGREE 5 WITH A CUSP

Author(s) -

Ali Atabaigi,

Hamid R. Z. Zangeneh

Publication year - 2011

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2011021

Subject(s) - mathematics , bifurcation , cusp (singularity) , mathematical analysis , degree (music) , pitchfork bifurcation , class (philosophy) , limit (mathematics) , pure mathematics , bifurcation theory , physics , geometry , nonlinear system , quantum mechanics , acoustics , artificial intelligence , computer science

This paper deals with small perturbations of a class of hyper-elliptic Hamiltonian system, which is a Li e nard system of the form \(\dot{x}=y,\) \(\;\dot{y}=Q_1(x)+\varepsilon yQ_2(x)\) with \(Q_1\) and \(Q_2\) polynomials of degree 4 and 3, respectively. It is shown that this system can undergo degenerated Hopf bifurcation and Poincar e bifurcation, which emerge at most three limit cycles for \(\varepsilon\) sufficiently small.

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