Pattern formation in three species food web model in spatiotemporal domain with Beddington–DeAngelis functional response
Articles
Randhir Singh Baghel
Jiwaji University, India
Joydip Dhar
ABV – Indian Institute of Information Technology and Management
Published 2014-04-10
https://doi.org/10.15388/NA.2014.2.1
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Keywords

food web
Hopf-bifurcation
reaction diffusion mechanism
spatial patterns
higher order stability

How to Cite

Baghel R. S. and Dhar J. (2014) “Pattern formation in three species food web model in spatiotemporal domain with Beddington–DeAngelis functional response”, Nonlinear Analysis: Modelling and Control, 19(2), pp. 155-171. doi: 10.15388/NA.2014.2.1.

Abstract

A mathematical model is proposed to study a three species food web model of preypredator system in spatiotemporal domain. In this model, we have included three state variables, namely, one prey and two first order predators population with Beddington-DeAngelis predation functional response. We have obtained the local stability conditions for interior equilibrium and the existence of Hopf-bifurcation with respect to the mutual interference of predator as bifurcation parameter for the temporal system. We mainly focus on spatiotemporal system and provided an analytical and numerical explanation for understanding the diffusion driven instability condition. The different types of spatial patterns with respect to different time steps and diffusion coefficients are obtained. Furthermore, the higher-order stability analysis of the spatiotemporal domain is explored.

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