Nontrivial Effect of Time-Varying Migration on the Three Species Prey-Predator System 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, and the project of Academic and technical leaders candidate of Anhui Province under Grant No. 2017H117

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 extinc...

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Bibliographic Details
Published in:Communications in theoretical physics 2019-01, Vol.71 (1)
Main Authors: Jin, Meng, Xu, Fei, Shen, Chuan-Sheng, Zhang, Ji-Qian, Wang, Cheng-Yu
Format: Article
Language:English
Subjects:
extinction critical phenomenon
Hopf bifurcation
prey-predator model
time-varying migration
Online Access:Get full text
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Summary: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.
ISSN:0253-6102
DOI:10.1088/0253-6102/71/1/127