Modeling wind effect and herd behavior in a predator–prey system with spatiotemporal dynamics
Department of Mathematics, Indian Institute of Engineering Science and Technology, 711103, Shibpur, Howrah, India
2 Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097, Warszawa, Poland
Accepted: 30 July 2022
Published online: 23 August 2022
In this work, we unveiled some important aspects of a predator–prey system in a windy environment considering the herd geometry of prey species by constructing a mathematical model of the proposed system under consideration. As the first of the study, we have shown the positivity and boundedness property of the solutions of the modified new system. Analytical and numerical experiments exhibit the dependence of equilibrium biomass on the strength of wind and geometry of the herd shape. The existence of trans-critical and Hopf bifurcation has been observed for a smooth change in the windy environment. Sensitivity analysis has been carried out to explore the significant parameters that affect the predator population density. Moreover, we have studied the spatially extended system with a windy environment and herd behavior. The existence of Hopf bifurcation is proved in the system, theoretically and numerically. Turing patterns are not possible in the system; however, interesting non-Turing patterns are obtained for different herd behaviors in a windy environment. The resulting non-Turing patterns are irregular patchy chaotic patterns as corresponding chaotic spatial attractors obtained in the spatially extended system. Hence, the spatially extended system exhibits interesting spatiotemporal dynamics with a windy environment and herd behavior. These dynamics help better understand predator–prey interactions in a real environment.
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