带有Michaelis-Menten型收获项的Lotka-Volterra捕食-食饵模型的稳定性和Hopf分支

Stability and Hopf bifurcation of a Lotka-Volterra predator-prey model with Michaelis-Menten type harvesting term

基于种群Lotka-Volterra捕食-食饵模型增长的假设,构建了一个带有食饵收获项的Lotka-Volterra模型.首先探讨了该模型平衡点的存在性和稳定性,然后讨论了一个正平衡点附近产生的Hopf分支,最后通过数值模拟验证了理论分析结果.

Based on the assumption of Lotka-Volterra predator-prey model,a Lotka-Volterra model with prey harvesting is constructed in this paper.First,the existence and stability of the equilibrium points of the model are discussed,and then the Hopf bifurcation generated near a positive equilibrium point is discussed.Finally,the numerical simulation is given to verify the theoretical analysis.