Some bifurcation methods of finding limit cycles

  • 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.

    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

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  • 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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    © 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)
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