考虑恐惧效应和人为捕获或投放的食饵-捕食者模型

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中图分类号：0175.1 文献标志码：A

A predator-prey model with fear effect anthropogenic harvesting or stocking

ZHANG Minghui， MA Jiying， XU Shenlong （ ， ， 2Ooo93， ）

Abstract： The predator-prey model with constant harvesting （or stocking） was investigated， the impact fear eect on the dynamical behavior the system was considered. Firstly，the equilibrium points their local stability were analyzed， the boundary equilibrium would become a degenerate saddle-node under certain conditions was verified. Secondly， by introducing a series transmations utilizing normal m theory， it was proved that the system could undergo saddle-node bifurcation， Hopf bifurcation degenerate Hopf bifurcation under certain conditions. The theoretical results indicate that some parameter values the system has exactly two limit cycles， which the outer limit cycle is stable. Finally， the phase portraits the system were depicted by MATLAB. Numerical simulations show that a low level fear can lead to the extinction populations， that is， an appropriate fear effect is beneficial the coexistence two populations.

Keywords： predator-prey model; fear efect; constant harvesting （stocking） ; Hopf bifurcation; phase portrait

1 模型的建立

食饵-捕食者模型是描述捕食者与其被捕食者（食饵）之间相互作用的种群动力学模型，捕食与被捕食关系是数学生态学中研究的一个重要关系[1-3]。（剩余11649字）