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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

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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Keywords 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. Mathematical Biosciences and Engineering, 2006, 3(1): 67-77. doi: 10.3934/mbe.2006.3.67


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Copyright Info: 2006, Maoan Han, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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