Bifurcation Analysis Of A Predator-Prey Model With Holling-Type Feedback

In this paper, we analysis bifurcations of a predator-prey model with Holling-Ⅱ type feedback by nonlinear theory and method (mainly normal form theory and homo logy method), and reveal the mutual effect of two species densities and the development trend of populations by theorems of dynamical system. This work provides a theoretic support for preventing population extinction and maintaining population stability.In this paper, by introducing harvesting rate parameters, we derive out the Holling-Ⅱ type predator-prey model with predator and prey harvest, respectively. We study the systems’ Equilibria and their stabilities, and then we investigate several bifurcations taken place in the modes for each of these two cases. All of these reveal rich dynamical behaviors of Holling-Ⅱ type biological models with harvest and verify the significance of harvesting rate parameters in preventing population extinction and maintaining population stability. Thus the results provide theoretical supports for population ecology.