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Open AccessArticle

Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species

Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russia
INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 101;
Received: 13 December 2019 / Accepted: 2 January 2020 / Published: 7 January 2020
(This article belongs to the Special Issue Partial Differential Equations in Ecology: 80 Years and Counting)
Investigation of interacting populations is an active area of research, and various modeling approaches have been adopted to describe their dynamics. Mathematical models of such interactions using differential equations are capable to mimic the stationary and oscillating (regular or irregular) population distributions. Recently, some researchers have paid their attention to explain the consequences of transient dynamics of population density (especially the long transients) and able to capture such behaviors with simple models. Existence of multiple stationary patches and settlement to a stable distribution after a long quasi-stable transient dynamics can be explained by spatiotemporal models with nonlocal interaction terms. However, the studies of such interesting phenomena for three interacting species are not abundant in literature. Motivated by these facts here we have considered a three species prey–predator model where the predator is generalist in nature as it survives on two prey species. Nonlocalities are introduced in the intra-specific competition terms for the two prey species in order to model the accessibility of nearby resources. Using linear analysis, we have derived the Turing instability conditions for both the spatiotemporal models with and without nonlocal interactions. Validation of such conditions indicates the possibility of existence of stationary spatially heterogeneous distributions for all the three species. Existence of long transient dynamics has been presented under certain parametric domain. Exhaustive numerical simulations reveal various scenarios of stabilization of population distribution due to the presence of nonlocal intra-specific competition for the two prey species. Chaotic oscillation exhibited by the temporal model is significantly suppressed when the populations are allowed to move over their habitat and prey species can access the nearby resources. View Full-Text
Keywords: prey–predator; diffusion; nonlocal interaction; Turing instability; spatiotemporal pattern prey–predator; diffusion; nonlocal interaction; Turing instability; spatiotemporal pattern
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Manna, K.; Volpert, V.; Banerjee, M. Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species. Mathematics 2020, 8, 101.

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