Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters

Meilan Cai; Maoan Han

doi:10.3934/cpaa.2020257

Article Contents

2021, Volume 20, Issue 1: 55-75. Doi: 10.3934/cpaa.2020257

This issue Previous Article A note on Riemann-Liouville fractional Sobolev spaces Next Article Scattering of the focusing energy-critical NLS with inverse square potential in the radial case

Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters

Meilan Cai^1, and
Maoan Han^2,1, ,

1.
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
2.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China

^* Corresponding author
^* Corresponding author

Received: February 29, 2020

Revised: July 31, 2020

Early access: October 2020

Published: January 2021

This work was supported by National Nature Science Foundation of China (11931016 and 11771296)

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Abstract

In this paper, we concern with the problem of limit cycle bifurcation for a class of piecewise smooth cubic systems. Using the first order Melnikov function we prove that at least thirteen limit cycles can be bifurcated from periodic solutions surrounding the center.

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Mathematics Subject Classification: Primary: 34C05, 34C07; Secondary: 37G15.

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Figure 1.1. Phase portrait of $ (1.3)|_{\varepsilon = \lambda = 0} $

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Figure 2.1. The periodic orbit $ L_{\lambda} $ of (2.1)$ |_{\varepsilon = 0} $

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Figure 3.1. The sketches of functions $ W_{i}(h) $, $ i = 1, 2, \cdots, 8 $

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