Codimension-one and codimension-two bifurcations of a discrete Leslie-Gower type predator-prey model

作者：Yuhua Long, Xiaofeng Pang, Qinqin Zhang · 发表于：Discrete and Continuous Dynamical Systems - B · 年份：2024 · DOI：10.3934/dcdsb.2024132 · 被引用次数：14 · 研究领域：Mathematical and Theoretical Epidemiology and Ecology Models、Aquatic and Environmental Studies、Quantum chaos and dynamical systems

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.