一类具有恐惧效应的离散捕食系统的稳定性分析  

Stability of a discrete predator-prey system with fear effect

作　　者：张雪妮 刘俊利[1] 刘白茹 ZHANG Xueni;LIU Junli;LIU Bairu(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2023年第4期89-97,107,共10页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基础研究计划项目(2021JM-445);陕西省杰出人才资助项目(10701000506);西安工程大学研究生创新基金(chx2021033)。

摘　　要：为了研究恐惧效应和捕食者之间的合作狩猎对捕食系统的影响,建立了一类具有恐惧效应和合作狩猎的离散捕食者-食饵模型。利用笛卡尔符号法则讨论了系统平衡点的存在性,分析了平衡点的稳定性;运用中心流形定理和分岔理论分析了Flip和Neimark-Sacker分岔的存在性条件。数值模拟验证了理论结果的有效性,并且表明系统会呈现双稳状态。In order to study the impact of fear effect and hunting cooperation between predators on the predator-prey system,a discrete predator-prey model with fear effect and hunting cooperation was established.Via the Descartes'rule of signs,the existence of equilibria was given;and the stability of equilibria was analyzed.By the center manifold theorem and the bifurcation theorem,the existence conditions of the Flip and Neimark-Sacker bifurcation were discussed.Finally,numerical simulations were carried out to verify the theoretical results.It also shows that the system is bistable.

关 键 词：捕食者-食饵系统 恐惧效应 合作狩猎 Flip分岔 NEIMARK-SACKER分岔 

分 类 号：O175.1[理学—数学]