具恐惧效应和食饵保护域的扩散捕食者-食饵系统动力学性质分析  

Dynamics of a diffusive predator-prey system with fear effect and protection zone

作　　者：吕伟 张继民[1] Lü Wei;ZHANG Jimin(School of Mathematical Science,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2020年第3期283-289,共7页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11201128);黑龙江省自然科学基金资助项目(LH2019A022)。

摘　　要：恐惧效应和建立食饵空间保护域在捕食者-食饵系统动力学研究中具有重要作用。研究一类具恐惧效应和食饵保护域的扩散捕食者-食饵系统的动力学性质。给出系统解的长时间性质,如解的全局存在性和有界性、系统的持续生存、系统半平凡解的稳定性、正稳态解的不存在性。最后利用稳态分歧理论,建立系统非常值解的存在性。Fear effect and space protection zone of prey play an important role in the study of predator-prey systems. The dynamic properties of a diffusive predator-prey system with fear effect and prey protection zone are investigated. The long-time properties of the solutions are given, such as global existence and boundedness of the solutions, permanence of the system, the stability of the semi-trivial solution of the system and the nonexistence of positive steady-state solutions. By using the steady-state bifurcation theory, the existence of non-constant steady-state solution of the system is presented.

关 键 词：捕食者-食饵系统 恐惧效应 保护域 稳定性 分歧理论 

分 类 号：O29[理学—应用数学]