Some bifurcation methods of finding limit cycles

Maoan Han; Tonghua Zhang

doi:10.3934/mbe.2006.3.67

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2006, Volume 3, Issue 1: 67-77. Doi: 10.3934/mbe.2006.3.67

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Some bifurcation methods of finding limit cycles

Maoan Han^1, and
Tonghua Zhang^2,

1.
Department of Mathematics, Shanghai Normal University, Shanghai 200234
2.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240 PR

Received: December 31, 2004

Revised: March 31, 2005

Published: October 2005

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Abstract

In this paper we outline some methods of finding limit cycles for planar autonomous systems with small parameter perturbations. Three ways of studying Hopf bifurcations and the method of Melnikov functions in studying Poincaré bifurcations are introduced briefly. A new method of stability-changing in studying homoclinic bifurcation is described along with some interesting applications to polynomial systems.

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Mathematics Subject Classification: 34C07.

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