Local dynamics and coexistence of predator–prey model with directional dispersal of predator

Kwangjoong Kim; Wonhyung Choi; Kwangjoong Kim; Wonhyung Choi

doi:10.3934/mbe.2020351

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6737-6755. doi: 10.3934/mbe.2020351

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Research article Special Issues

Local dynamics and coexistence of predator–prey model with directional dispersal of predator

Kwangjoong Kim ¹,
Wonhyung Choi ^{2,
,
,}

1.
College of General Education, Kookmin University, 77, Jeongneung-ro, Seoul, 02707, Korea
2.
Industry-Academic Cooperation Foundation, Kookmin University, 77, Jeongneung-ro, Seoul, 02707, Korea
² The author is now with the Department of Mathematics, Tamkang University, 151, Yingzhuan Road, Tamsui, New Taipei City, 251301, Taiwan.

Received: 15 June 2020 Accepted: 23 September 2020 Published: 30 September 2020

In this paper, we study the effect of directional dispersal of a predator on a predator– prey model. The prey is assumed to have traits making it undetectable to the predator and difficult to chase the prey directly. Directional dispersal of the predator is described when the predator has learned the high hunting efficiency in certain areas, thereby dispersing toward these areas instead of directly chasing the prey. We investigate the stability of the semi-trivial solution and the existence of a coexistence steady-state. Moreover, we show that the predator that moves toward a high-predation area may make the predators survive under the condition the predators cannot survive when they disperse randomly. The results are obtained through eigenvalue analysis and fixed-point index theory. Finally, we present the numerical simulation and its biological interpretations based on the obtained results.

Keywords:

Citation: Kwangjoong Kim, Wonhyung Choi. Local dynamics and coexistence of predator–prey model with directional dispersal of predator[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6737-6755. doi: 10.3934/mbe.2020351

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Abstract

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