Nontrivial Effect of Time-Varying Migration on the Three Species Prey-Predator System  

作　　者：金梦 徐飞 申传胜 张季谦 王成宇 

机构地区：[1]School of Mathematics and Computational Science, Anqing Normal University [2]College of Physics and Electronic Information, Anhui Normal University

出　　处：《Communications in Theoretical Physics》2019年第1期127-131,共5页理论物理通讯（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No.11475003;the Key project of cultivation of leading talents in Universities of Anhui Provence under Grant Nos.gxfxZD2016174,gxbjZD2016014;the project of Academic and technical leaders candidate of Anhui Province under Grant No.2017H117

摘　　要：Migration is ubiquitous in ecosystem and often plays an important role in biological diversity. In this work,by introducing a time-varying migration rate associated with the difference of subpopulation density into a prey, we study the Hopf bifurcation and the critical phenomenon of predator extinction of the three species prey-predator system,which consists of a predator, a prey and a mobile prey. It is found that the system with migration exhibits richer dynamic behaviors than that without migration, including two Hopf bifurcations and two limit cycles. Interestingly,the parameters of migration have a drastically influence on the critical point of predator extinction, determining the coexistence of species. Moreover, the population evolution dynamics of one-dimensional multiple prey-predator system are also discussed.Migration is ubiquitous in ecosystem and often plays an important role in biological diversity. In this work,by introducing a time-varying migration rate associated with the difference of subpopulation density into a prey, we study the Hopf bifurcation and the critical phenomenon of predator extinction of the three species prey-predator system,which consists of a predator, a prey and a mobile prey. It is found that the system with migration exhibits richer dynamic behaviors than that without migration, including two Hopf bifurcations and two limit cycles. Interestingly,the parameters of migration have a drastically influence on the critical point of predator extinction, determining the coexistence of species. Moreover, the population evolution dynamics of one-dimensional multiple prey-predator system are also discussed.

关 键 词：PREY-PREDATOR model TIME-VARYING MIGRATION HOPF BIFURCATION EXTINCTION critical phenomenon 

分 类 号：O4[理学—物理]