一类带有恐惧效应的捕食模型正解的分歧及稳定性

Bifurcation solutions and stability of apredator-prey model with fear effect

考虑了一类带有恐惧效应的捕食-食饵模型的共存态问题.利用谱分析和分歧理论的方法,以m为分歧参数,讨论了系统在半平凡解附近出现分歧现象.运用线性算子的扰动理论和分歧解的稳定性理论给出分歧解的稳定性.得出系统在半平凡解附近出现分歧现象且局部分歧解是无条件稳定的.

The coexistence of the predator-prey model with fear effect is considered.By the method of spectral analysis and bifurcation theory,the bifurcation at the steady-state solutions is acquired by treating m as bifurcation parameters.Some stability results of the bifurcation solutions are obtained by using perturbation theory of linear operators and stability theory of bifurcation solutions.The results show that this system arises bifurcation phennmenon at the steady-state solution,and this bifurcation solution is unconditionally stable.