Limit Cycles of Perturbed Cubic Isochronous Center via the Second Order Averaging Method-Reference-Cited by-同舟云学术

Limit Cycles of Perturbed Cubic Isochronous Center via the Second Order Averaging Method

Published:2014-03 Issue:03 Volume:24 Page:1450035
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Li Shimin¹,Zhao Yulin²

Affiliation:

1. School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, P. R. China

2. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China

Abstract

In this paper, we bound the number of limit cycles for a class of cubic reversible isochronous system inside the class of all cubic polynomial differential systems. By applying the averaging method of second order to this system, it is proved that at most eight limit cycles can bifurcate from the period annulus. Moreover, this bound is sharp.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127414500357

Reference11 articles.

1. Averaging methods for finding periodic orbits via Brouwer degree

2. Limit cycles of cubic polynomial vector fields via the averaging theory

3. Linear Estimation of the Number of Zeros of Abelian Integrals for Some Cubic Isochronous Centers

4. HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS

5. Quadratic Perturbations of a Quadratic Reversible Lotka–Volterra System

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