Some bifurcation methods of finding limit cycles

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/192075

Title: Some bifurcation methods of finding limit cycles
Author(s): Han, Maoan; Zhang, Tonghua
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 Poincare bifurcations are introduced briefly. A new method of stabilitychanging in studying homoclinic bifurcation is described along with some interesting applications to polynomial systems.
Publication type: Journal article
Source: Mathematical Biosciences and Engineering, Vol. 3, no. 1 (Jan 2006), pp. 67-77
Publication year: 2006
FOR Code(s): 0102 Applied Mathematics
Keyword(s): Hilbert's 16th problem; Homoclinic bifurcation; Hopf bifurcations; Limit cycle; Melnikov function; Poincare bifurcations; Stability-changing
Publisher: American Institute of Mathematical Sciences
ISSN: 1547-1063
Publisher URL: http://www.mbejournal.org/StaticLinks/Vol-3-No-1.htm