Limit cycle bifurcations for piecewise smooth integrable differential systems

Jihua Yang; Liqin Zhao

doi:10.3934/dcdsb.2017123

Article Contents

2017, Volume 22, Issue 6: 2417-2425. Doi: 10.3934/dcdsb.2017123

This issue Previous Article Numerical solutions of viscoelastic bending wave equations with two term time kernels by Runge-Kutta convolution quadrature Next Article Invariant measures for complex-valued dissipative dynamical systems and applications

Limit cycle bifurcations for piecewise smooth integrable differential systems

Jihua Yang^1, , and
Liqin Zhao^2,

1.
School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000, China
2.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Author Bio: E-mail address: zhaoliqin@bnu.edu.cn
Jihua Yang, E-mail address: jihua1113@163.com
Jihua Yang, E-mail address: jihua1113@163.com

Received: May 2016

Revised: March 2017

Published: May 2017

The first author is supported by NSFC(11671040,11601250), the Visual Learning Young Researcher of Ningxia, the Science and Technology Pillar Program of Ningxia(KJ[2015]26(4)) and the Key Program of Ningxia Normal University(NXSFZD1708); The second author is supported by NSFC(11671040).

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Abstract

In this paper, we study a class of piecewise smooth integrable non-Hamiltonian systems, which has a center. By using the first order Melnikov function, we give an exact number of limit cycles which bifurcate from the above periodic annulus under the polynomial perturbation of degree n.

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Mathematics Subject Classification: Primary:34C07, 34C05.

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