具有恐惧效应和空间异质捕食-食饵模型的稳态解

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.

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

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.