Nontrivial Effect of Time-Varying Migration on the Three Species Prey-Predator System |
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Authors: | Meng Jin Fei Xu Chuan-Sheng Shen Ji-Qian Zhang Cheng-Yu Wang |
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Institution: | 1. School of Mathematics and Computational Science, Anqing Normal University, Anqing 246011, China;
2. College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China |
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Abstract: | 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. |
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Keywords: | prey-predator model time-varying migration Hopf bifurcation extinction critical phenomenon |
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