Impacts of the Dispersal Delay on the Stability of the Coexistence Equilibrium of a Two-Patch Predator–Prey Model with Random Predator Dispersal

  • Ali Mai
  • Guowei Sun
  • Lin WangEmail author


In this paper, we study a predator–prey system with random predator dispersal over two habitat patches. We show that in most cases the dispersal delay does not affect the stability and instability of the coexistence equilibrium. However, if the mean time that the predator spent in one patch is much shorter than the timescale of reproduction of the prey and is larger than the double mean time of capture of prey, the dispersal delay can induce stability switches such that an otherwise unstable coexistence equilibrium can be stabilized over a finite number of stability intervals.


Predator–prey Random dispersal Dispersal delay Stability switch 



The authors would like to thank the anonymous referee for his/her valuable comments and suggestions, which greatly helped us improve the presentation of this paper. This work is partially supported by National Natural Science Foundation of China (No. 11526183), China Scholarship Council (201608140214), Foundation of Yuncheng University (YQ-2017003), Biomathematics Laboratory of Yuncheng University (SWSX201502, SWSX201602) and by a discovery grant from NSERC.


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© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information TechnologyYuncheng UniversityYunchengChina
  2. 2.Department of Mathematics and StatisticsUniversity of New BrunswickFrederictonCanada

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