具有恐惧效应和空间异质捕食-食饵模型的稳态解

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (4): 775-783.

具有恐惧效应和空间异质捕食-食饵模型的稳态解

张萌萌, 李善兵

西安电子科技大学数学与统计学院, 西安 710126

收稿日期:2021-10-04 出版日期:2022-07-26 发布日期:2022-07-26
通讯作者: 李善兵 E-mail:lishanbing@xidian.edu.cn

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

ZHANG Mengmeng, LI Shanbing

College of Mathematics and Statistics, Xidian University, Xi’an 710126, China

Received:2021-10-04 Online:2022-07-26 Published:2022-07-26

摘要/Abstract

摘要： 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.

关键词: 捕食-食饵模型, Holling Ⅲ函数, 恐惧效应, 空间异质

Abstract: 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.

Key words: predator-prey model, Holling Ⅲ function, fear effect, spatial heterogeneity

中图分类号:

张萌萌, 李善兵. 具有恐惧效应和空间异质捕食-食饵模型的稳态解[J]. 吉林大学学报(理学版), 2022, 60(4): 775-783.

ZHANG Mengmeng, LI Shanbing. Steady State Solutions of Predator-Prey Model with Fear Effect and Spatial Heterogeneity[J]. Journal of Jilin University Science Edition, 2022, 60(4): 775-783.

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