On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model-Reference-Cited by-同舟云学术

On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model

Published:2016-09 Issue:10 Volume:26 Page:1650168
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Sheng Lijuan¹,Han Maoan¹,Romanovsky Valery²³

Affiliation:

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

2. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000, Slovenia

3. Faculty of Natural Science and Mathematics, University of Maribor, Koroška Cesta 160, SI-2000 Maribor, Slovenia

Abstract

In this paper, we study the number of limit cycles by perturbing a Liénard model [Formula: see text] [Formula: see text], where [Formula: see text] is piecewise smooth. Under the assumption that the unperturbed Liénard type system has a family of periodic orbits, we first deduce the expression for its first order Melnikov function, and then obtain the maximum number of limit cycles bifurcating from the period annulus.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127416501686

Reference30 articles.

1. Descartes' Rule of Signs Revisited

2. Polynomial systems: a lower bound for the Hilbert numbers

3. ON THE NUMBER AND DISTRIBUTION OF LIMIT CYCLES IN A CUBIC SYSTEM

4. A new cubic system having eleven limit cycles

5. ON THE NUMBER OF LIMIT CYCLES IN NEAR-HAMILTONIAN POLYNOMIAL SYSTEMS

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