Bifurcation of Limit Cycles from a Polynomial Degenerate Center-Reference-Cited by-同舟云学术

Bifurcation of Limit Cycles from a Polynomial Degenerate Center

Published:2010-08-01 Issue:3 Volume:10 Page:597-609
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Buică Adriana¹,Giné Jaume²,Llibre Jaume³

Affiliation:

1. Department of Applied Mathematics, Babeş-Bolyai University RO-400084 Cluj-Napoca, Romania

2. Departament de Matemàtica, Universitat de Lleida Av. Jaume II, 69, 25001 Lleida, Catalonia, Spain

3. Departament de Matemàtiques, Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona, Catalonia, Spain

Abstract

Abstract Using Melnikov functions at any order, we provide upper bounds for the maximum number of limit cycles bifurcating from the period annulus of the degenerate center ẋ = −y((x2 + y2)/2)m and ẏ = x((x2 + y2)/2)m with m ≥ 1, when we perturb it inside the whole class of polynomial vector fields of degree n. The positive integers m and n are arbitrary. As far as we know there is only one paper that provide a similar result working with Melnikov functions at any order and perturbing the linear center ẋ = −y, ẏ = x.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2010-0305/pdf

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