改进的HollingⅡ类功能性捕食模型的定性分析

A qualitative analysis on the improved Holling Ⅱ functional predator-prey model

研究有关种群、群落、生态系统的稳定性问题。对具有常数收获率的HollingⅡ类功能性捕食模型进行改进并分析,应用微分方程的定性理论,讨论本模型平衡点的存在性和稳定性,通过理论推导得到极限环不存在的判定定理。并在满足各定理条件下,分别取适当的参数值,利用Matlab数学软件对模型进行数值模拟,从而验证各平衡点定理的正确性。

The stability problems of the population, community, ecological system are studied. Holling II functional predator prey model with constant harvest rate is improved and analyzed. The existence and stability of equilibrium point are discussed firstly in terms of the qualitative theory of differential equations. Secondly, judgment theorems about nonexistence of limit cycle are given by theory deduction. Finally, numerical simulation is executed by Matlab software through choosing the proper parameters respectively under the conditions of meeting each theorem. Experimental results show that the new model is more stable and also show the correctness of the theory.