Codimension-one and codimension-two bifurcations of a discrete Leslie-Gower type predator-prey model
Yuhua Long, Xiaofeng Pang, Qinqin Zhang
Abstract
In the present paper, by the forward Euler scheme, we propose a discrete-time Leslie-Gower type predator-prey model of ratio-dependent functional response and Michalis-Menten function prey harvesting. We not only investigate the existence and stability of equilibria of the model, but also derive codimension-one and codimension-two bifurcations of interior equilibria, including fold, flip, Hopf, 1:1 strong resonance, fold-flip and 1:2 strong resonance bifurcations by the center manifold method and bifurcation theorem. Moreover, we provide numerical simulations including bifurcation diagrams and phase portraits to illustrate the correctness of the obtained theoretical results and reveal the complex dynamic behaviours of discrete models.