Limit Cycles for a Discontinuous Quintic Polynomial Differential System

Bo Huang

doi:10.1007/s12346-018-00312-6

Limit Cycles for a Discontinuous Quintic Polynomial Differential System

Bo Huang^*

^*Corresponding author for this work

School of Mathematical Sciences

New York University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this article, we study the maximum number of limit cycles for a discontinuous quintic differential system. Using the first-order averaging method, we explain how limit cycles can bifurcate from the period annulus around the center of the considered system when it is perturbed inside a class of discontinuous quintic polynomial differential systems. Our results show that the lower bound and the upper bound of the number of limit cycles, 8 and 10 respectively, that can bifurcate from the period annulus around the center.

Original language	English
Pages (from-to)	769-792
Number of pages	24
Journal	Qualitative Theory of Dynamical Systems
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/s12346-018-00312-6
State	Published - 1 Dec 2019

Keywords

Averaging method
Center
Discontinuous quintic system
Limit cycle
Period annulus

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title = "Limit Cycles for a Discontinuous Quintic Polynomial Differential System",

abstract = "In this article, we study the maximum number of limit cycles for a discontinuous quintic differential system. Using the first-order averaging method, we explain how limit cycles can bifurcate from the period annulus around the center of the considered system when it is perturbed inside a class of discontinuous quintic polynomial differential systems. Our results show that the lower bound and the upper bound of the number of limit cycles, 8 and 10 respectively, that can bifurcate from the period annulus around the center.",

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AB - In this article, we study the maximum number of limit cycles for a discontinuous quintic differential system. Using the first-order averaging method, we explain how limit cycles can bifurcate from the period annulus around the center of the considered system when it is perturbed inside a class of discontinuous quintic polynomial differential systems. Our results show that the lower bound and the upper bound of the number of limit cycles, 8 and 10 respectively, that can bifurcate from the period annulus around the center.

KW - Averaging method

KW - Center

KW - Discontinuous quintic system

KW - Limit cycle

KW - Period annulus

UR - https://www.scopus.com/pages/publications/85069794641

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M3 - 文章

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IS - 3

ER -

Limit Cycles for a Discontinuous Quintic Polynomial Differential System

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Keywords

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