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Mathematical Biosciences and Engineering

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

  • 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.

    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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