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Invasion analysis on a predator–prey system in open advective environments

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Abstract

We investigate a reaction–diffusion–advection system which characterizes the interactions between the predator and prey in advective environments, such as streams or rivers. In contrast with non-advective environments, the dynamics of this system is more complicated. It turns out that there exists a critical mortality rate of the predator and two critical advection rates, which classify the dynamic behavior of this system into two or three scenarios, that is, (i) both populations go extinct; (ii) the predator can not invade and the prey survives in the long run; (iii) the predator can invade successfully when rare and it will coexist permanently with the prey. Specially, the predator can invade successfully when rare if both the mortality rate of the predator and the advection rate are suitably small. Furthermore, by the global bifurcation theory and some auxiliary techniques, the existence and uniqueness of coexistence steady states of this system are established. Finally, by means of numerical simulations, the effects of diffusion on the dynamics of this system are investigated. The numerical results show that the random dispersals of both populations favor the invasion of the predator.

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Acknowledgements

The authors are very grateful to the anonymous referees and the handling associate editor for their kind and valuable suggestions leading to a substantial improvement of the manuscript. H. Nie was supported by the National Natural Science Foundation (No. 11671243). B. Wang was supported by the National Natural Science Foundation (No. 11801436) and Natural Science Basic Research Plan in Shaanxi Province of China (No. 2019JQ-346). J. H. Wu was supported by the National Natural Science Foundation of China (No. 11771262).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, Shaanxi, China

    Hua Nie & Jianhua Wu

  2. College of Science, Xi’an University of Science and Technology, Xi’an, 710054, China

    Biao Wang

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  1. Hua Nie
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  2. Biao Wang
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  3. Jianhua Wu
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Correspondence to Jianhua Wu.

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Nie, H., Wang, B. & Wu, J. Invasion analysis on a predator–prey system in open advective environments. J. Math. Biol. 81, 1429–1463 (2020). https://doi.org/10.1007/s00285-020-01545-3

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  • DOI: https://doi.org/10.1007/s00285-020-01545-3

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