Bulletin of Mathematical Biology

, Volume 80, Issue 4, pp 906–925 | Cite as

Analysis of a Prey–Predator Model with Non-local Interaction in the Prey Population

Original Article
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Abstract

Non-local reaction–diffusion equation is an important area to study the dynamics of the individuals which compete for resources. In this paper, we describe a prey-dependent predator–prey model with Holling type II functional response with a generalist predator. In particular, we want to see the behavior of the system in the presence of non-local interaction. Introduction of non-local intraspecific competition in prey population leads to some new characteristics in comparison with the local model. Comparisons have been made between the local and non-local interactions of the system. The range of non-local interaction enlarges the parametric domain on which stationary patterns exist. The periodic oscillation for the local model in the Hopf domain can be stabilized by suitable limit of strong non-local interaction. An increase in the range of non-local interaction increases the Turing domain up to a certain level, and then, it decreases. Also, increasing the range of non-local interaction results in the overlap of nearby foraging areas and hence alters the size of the localized patches and formation of multiple stationary patches. Numerical simulations have been carried out to validate the analytical findings and to establish the existence of multiple stationary patterns, oscillatory solution, two-periodic solution and other spatiotemporal dynamics.

Keywords

Reaction–diffusion equation Non-local interaction Spatial Hopf bifurcation 

Notes

Acknowledgements

The work of the first author (S. Pal) is supported by DST INSPIRE FELLOWSHIP, REG. NO. IF150434.

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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIIT KanpurKanpurIndia

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