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Limit Cycles Bifurcations for a Class of 3-Dimensional Quadratic Systems

Limit Cycles Bifurcations for a Class of 3-Dimensional Quadratic Systems Our work is concerned with the Hopf bifurcation for a class of 3-dimensional quadratic symmetric vector field. By making use of singular values methods and computing carefully, we give the expressions of the first four focal values of the two singular point that system has. Both singular symmetric points can become fine foci of fourth order at the same time. Moreover, we obtain that from each one can bifurcate 4 small limit cycles under a certain coefficients’ perturbed condition, consequently, at most eight limit cycles can appear by simultaneous Hopf bifurcation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Limit Cycles Bifurcations for a Class of 3-Dimensional Quadratic Systems

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer Science+Business Media Dordrecht
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-014-9881-4
Publisher site
See Article on Publisher Site

Abstract

Our work is concerned with the Hopf bifurcation for a class of 3-dimensional quadratic symmetric vector field. By making use of singular values methods and computing carefully, we give the expressions of the first four focal values of the two singular point that system has. Both singular symmetric points can become fine foci of fourth order at the same time. Moreover, we obtain that from each one can bifurcate 4 small limit cycles under a certain coefficients’ perturbed condition, consequently, at most eight limit cycles can appear by simultaneous Hopf bifurcation.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Apr 18, 2014

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