具有恐惧效应和空间异质捕食-食饵模型的稳态解

Steady State Solutions of Predator-Prey Modelwith Fear Effect and Spatial Heterogeneity

考虑一类具有恐惧效应和空间异质的捕食-食饵模型.首先,利用Riesz-Schauder理论给出平凡解和半平凡解的局部渐近稳定性;其次,利用比较原理给出平凡解和半平凡解的全局吸引性;最后,利用不动点定理给出正稳态解的存在性.结果表明,恐惧效应和空间异质对模型的稳态解性质有明显影响.

We considered a predator-prey model with fear effect and spatial heterogeneity.Firstly,we gave the local asymptotic stability of trivial and semi-trivial solutions by using Riesz-Schauder theory.Secondly,we gave the global attractivity of trivial and semi-trivial solutions by using the principle of comparison.Finally,we gave the existence of a positive steady-state solution by using the fixed point theorem.The results show that fear effect and spatial heterogeneity have significant effects on the properties of steady-state solutions of the model.