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.
Mathematical Biosciences and Engineering,
Vol. 3, no. 1 (Jan 2006), pp. 67-77