具有Holling-Tanner功能反应的捕食模型研究

Study on the Predator-prey Model with Holling-Tanner Functional Response

建立了具有状态反馈控制的比率依赖功能反应的Holling-Tanner捕食模型.首先,定义了该模型的庞加莱映射,讨论了其单调性、连续性、可微性、凸性以及不动点等性质;其次,利用脉冲微分方程几何理论和庞加莱映射的性质,分析了模型的阶1周期解的存在性、唯一性的充分条件,并给出阶1周期解全局稳定性的充要条件,在此基础上研究了阶k(k≥2)周期解的存在性;最后,通过数值模拟验证了理论结果的正确性.

In this paper,a Holling-Tanner predator-prey model with state-dependent feedback control and ratio-dependent functional response is established.Firstly,we define the Poincarémap of system,and prove the properties of monotonicity,continuity,differentiability,convexity and fixed point.Secondly,the impulsive differential equation theory is used to analyze the existence,uniqueness and global stability of order-1 periodic solution,and the necessary and sufficient condition for the global stability of the order-1 periodic solution are given.Based on this,the existence of the order-k(k≥2)periodic solutions is further studied.Finally,numerical simulation verifies the correctness of the theoretical results.