Some bifurcation methods of finding limit cycles

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

Previous Article Next Article

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

Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 November 2005
MSC : 34C07.

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

Related Papers:
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.
Reader Comments

Your name:*

Email:*
© 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)