On the Number of Limit Cycles Bifurcating from a Compound Polycycle-Reference-Cited by-同舟云学术

On the Number of Limit Cycles Bifurcating from a Compound Polycycle

Published:2020-06-15 Issue:07 Volume:30 Page:2050099
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Sheng Lijuan¹,Han Maoan¹²^ORCID,Tian Yun¹

Affiliation:

1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

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

Abstract

This paper focuses on the number of limit cycles bifurcating from a symmetrical compound polycycle with three saddles. We use two methods, the Melnikov function method and the method of stability-changing of a homoclinic loop or a double homoclinic loop to study this problem. We find 15 limit cycles and 16 limit cycles respectively with four alien limit cycles under certain conditions.

Funder

National Natural Science Foundation of China

Shanghai Rising-Star Program

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127420500996

Reference32 articles.

1. Alien limit cycles near a Hamiltonian 2-saddle cycle

2. On Hereditarily Indecomposable Banach Spaces