American Institute of Mathematical Sciences

Advanced
2006, 3(1): 67-77. doi: 10.3934/mbe.2006.3.67

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, China

Received  January 2005 Revised  April 2005 Published  November 2005

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.
Keywords: Melnikov function, homoclinic bifurcation, stability-changing, Hopf bifurcations., Poincare bifurcations, limit cycle, Hilbert's 16th problem.
Mathematics Subject Classification: 34C0.
Citation: Maoan Han, Tonghua Zhang. Some bifurcation methods of finding limit cycles. Mathematical Biosciences & Engineering, 2006, 3 (1) : 67-77. doi: 10.3934/mbe.2006.3.67
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