A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System

In this paper, we study Poincaré bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method, we give an estimation of the number of limit cycles which bifurcate from the period annul...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2020-08, Vol.19 (2), Article 61
Main Authors: Chen, Xiaoyan, Han, Maoan
Format: Article
Language:English
Subjects:
Bifurcations
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Hamiltonian functions
Mathematics
Mathematics and Statistics
Polynomials
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Summary:In this paper, we study Poincaré bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method, we give an estimation of the number of limit cycles which bifurcate from the period annulus between the center and the homoclinic loop under the piecewise polynomial perturbations of degree n . This result confirms a conjecture.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-020-00398-x