具有避难所的离散捕食者-食饵系统的动力学行为分析

Dynamical behavior analysis of a discrete predator⁃prey model with prey refuge

研究食饵具有恐惧效应和避难所的修正Leslie-Gower离散捕食者-食饵系统.首先,分析该模型平衡点的存在性和局部稳定性,通过严格的推导得到系统的食饵灭绝边界平衡点和正平衡点局部稳定的充分性条件.其次,分析在平衡点处存在的分支现象,讨论食饵灭绝边界平衡点处的跨临界分支和翻转分支,以及捕食者灭绝边界平衡点处的翻转分支.对马瑞等的研究成果进行完善.最后,通过数值模拟验证主要结果的可行性,探讨避难所对系统的影响.结果表明,避难所会促进捕食者种群与食饵种群的稳定共存,同步增长.

This paper focuses on a modified Leslie⁃Gower discrete predator⁃prey system with prey refuge and fear effect.Firstly,this paper analyzes the existence and local stability of the equilibria of the model,and obtains the sufficient conditions for the local stability of the prey free equilibrium point and the positive equilibrium point of the system through a rigorous derivation.Secondly,this paper analyzes the bifurcation at the equilibria,discusses the transcritical bifurcation and flip bifurcation at the prey free equilibrium point,and the flip bifurcation at the predator free equilibrium point.The corresponding results of RUI Ma,et al have been complement.Finally,feasibility of the main results is illustrated through numerical simulations.The results show that prey refuge can promote the stable coexistence and synchronous growth of predator and prey populations.