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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Dynamics of a Predator--Prey System with Wind Effect and Prey Refuge

Journal of Applied Nonlinear Dynamics 12(3) (2023) 427--440 | DOI:10.5890/JAND.2023.09.001

Eric M. Takyi$^{1}$, Kasey Cooper$^{1}$, Ava Dreher$^{2}$, Caroline McCrorey$^{3}$

$^{1}$ Department of Mathematics and Computer Science, Ursinus College, Collegeville, PA 19426, USA

$^{2}$ Department of Mathematics and Statistics, Binghamton University, Binghamton, NY 13902, USA

$^{3}$ Department of Mathematics, Bellarmine University, Louisville, KY 40205, USA

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Abstract

The natural environment of living organisms is not only affected by biotic factors but also by abiotic factors, including omnipresent wind. There has been less exploration on the effects of both biotic and abiotic factors on the dynamics of predator-prey interactions. In this work, we propose and study the dynamics of a predator-prey system incorporating wind effects and prey refuge. A refuge can be described as any strategy to avoid or reduce predation risks. We first prove positivity and boundedness of solutions for the system. We analyze the existence of equilibria under certain parametric restrictions. We also derive sufficient conditions for the global stability of the coexistence equilibrium using a suitable Lyapunov functional. Further dynamical analysis reveals that the system experiences local codimension one bifurcations including Hopf and transcritical bifurcations. Our findings show that when prey refuge is in use, it has a stabilizing effect on the system and also increases the equilibrium density of the prey population while the predator equilibrium density decreases. We also observe that the strength of wind flow has both stabilizing and destabilizing effects. We support our theoretical findings with numerical experiments and give their ecological implications.

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