Full Text: PDF
We study the phase portraits and Hopf bifurcations of the ratio-dependent Holling type III models with constant harvesting rates. We provide the ranges of the parameters involved under which all the equilibria be positive. We show that these positive equilibria can be saddles, topological saddles, saddle-nodes, stable (or unstable) nodes or focuses, weak centers or cusps, depending on the choices of the parameters. We compute the first Lyapunov number to obtain the subcritical and supercritical Hopf bifurcations of the models.
How to Cite this Article:
Guangping Luo, Kunquan Lan, Changrong Zhu, Bifurcations of ratio-dependent predator-prey holling type III systems with harvesting rates, Journal of Nonlinear Functional Analysis 2014 (2014), Article ID 16.