Local bifurcations of a ratio-dependent predator-prey system with Holling type III functional response

Abstract

In this paper a ratio-dependent predator-prey system with Holling type III functional response is discussed. We give parameter conditions for exact number of equilibria. The conditions for pitchfork bifurcation are given by the center manifold theory. Hopf bifurcations are discussed by computing Lyapunov coefficients. It is shown that at most one stable limit cycle occurs.