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Mathematics 2018, 6(3), 41; https://doi.org/10.3390/math6030041

Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey

1,†,* , 1,†
and
2,†
1
Department of Mathematics and Statistics, IIT Kanpur, Kanpur 208016, India
2
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 5 February 2018 / Revised: 1 March 2018 / Accepted: 5 March 2018 / Published: 8 March 2018
(This article belongs to the Special Issue Progress in Mathematical Ecology)
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Abstract

Spatiotemporal pattern formation in integro-differential equation models of interacting populations is an active area of research, which has emerged through the introduction of nonlocal intra- and inter-specific interactions. Stationary patterns are reported for nonlocal interactions in prey and predator populations for models with prey-dependent functional response, specialist predator and linear intrinsic death rate for predator species. The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of predators. We derive the conditions of the Turing and of the spatial Hopf bifurcation around the coexisting homogeneous steady-state and verify the analytical results through extensive numerical simulations. Bifurcations of spatial patterns are also explored numerically. View Full-Text
Keywords: prey-predator; nonlocal consumption; Turing bifurcation; spatial Hopf bifurcation; spatio-temporal pattern prey-predator; nonlocal consumption; Turing bifurcation; spatial Hopf bifurcation; spatio-temporal pattern
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Banerjee, M.; Mukherjee, N.; Volpert, V. Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey. Mathematics 2018, 6, 41.

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