具有恐惧效应的合作捕食模型动力学分析

Dynamical Analysis of a Cooperative Predation Model with Fear Effect

摘要: 本文研究了一类具有恐惧效应的合作捕食模型，其中包含一种食饵和两种捕食者。文章首先运用一般代数法求解平衡点，利用根的存在性定理和极限的方法证明平衡点存在性；其次利用线性化方法和Routh-Hurwitz判据给出ODE模型的平衡点渐近稳定性证明ODE的非平凡解在PDE下的Turing失稳条件，利用分歧定理证明PDE下存在非平凡解分支，并给出在ODE和PDE下各个平衡点稳定性条件对比。

Abstract: In this paper, a cooperative predation model incorporating one prey species and two predator species with fear effect is investigated. Firstly, algebraic methods are adopted to solve all equilibrium points, and the existence of these equilibria is verified via the existence theorem of polynomial roots and limit analysis. Secondly, linearization techniques together with the Routh-Hurwitz criterion are utilized to derive conditions for the asymptotic stability of equilibrium points of the ordinary differential equation (ODE) system. Furthermore, Turing instability conditions for non-trivial steady-state solutions of the corresponding partial differential equation (PDE) system are derived; the existence of bifurcating non-trivial solution branches for the PDE model is proven based on bifurcation theorems. Finally, stability conditions of each equilibrium point under the ODE framework and PDE framework are compared systematically.