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Global bifurcations in a perturbed cubic system withZ 2-symmetry

Global bifurcations in a perturbed cubic system withZ 2-symmetry In this paper we consider global and local bifurcations in disturbed planar Hamiltonian vector fields which are invariant under a rotation over π. All calculation formulas of bifurcation curves have been obtained. Various possible distributions and the existence of limit cycles and singular cycles in different parameter regions have been determined. It is shown that for a planar cubic differential system there are infinitely many parameters in the three-parameter space such that Hilbert numberH(3)≥11. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Global bifurcations in a perturbed cubic system withZ 2-symmetry

Acta Mathematicae Applicatae Sinica , Volume 8 (2) – Jul 13, 2005

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References (4)

Publisher
Springer Journals
Copyright
Copyright © 1992 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006149
Publisher site
See Article on Publisher Site

Abstract

In this paper we consider global and local bifurcations in disturbed planar Hamiltonian vector fields which are invariant under a rotation over π. All calculation formulas of bifurcation curves have been obtained. Various possible distributions and the existence of limit cycles and singular cycles in different parameter regions have been determined. It is shown that for a planar cubic differential system there are infinitely many parameters in the three-parameter space such that Hilbert numberH(3)≥11.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

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