Bifurcation of Limit Cycles by Perturbing Piecewise Linear Hamiltonian Systems with Piecewise Polynomials-Reference-Cited by-同舟云学术

Bifurcation of Limit Cycles by Perturbing Piecewise Linear Hamiltonian Systems with Piecewise Polynomials

Published:2023-04 Issue:05 Volume:33 Page:
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Chen Jiangbin¹²,Han Maoan¹^ORCID

Affiliation:

1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

2. Zhicheng College, Fuzhou University, Fuzhou, Fujian 350002, P. R. China

Abstract

In this paper, we study a class of piecewise smooth near-Hamiltonian systems with piecewise polynomial perturbations. We first give the expression of the first order Melnikov function, and then estimate the number of limit cycles bifurcated from periodic annuluses by Melnikov function method. In addition, we discuss the number of limit cycles that can appear simultaneously near both sides of a generalized homoclinic or generalized double homoclinic loop.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127423500591

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2. Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

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