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.
Highlights
Investigation of spatiotemporal pattern formation leads to understanding of the interesting and complex dynamics of prey-predator populations
We are interested to study pattern formation described by the nonlocal reaction-diffusion system of prey-predator interaction with the bistable reaction kinetics of prey in the absence of predators which are specialist in nature following Holling type-II functional response
Another interesting aspect of the stationary patterns arising through the Turing bifurcation for the spatiotemporal model with nonlocal interaction term is the existence of multiple stationary solutions for a particular value of M
Summary
Investigation of spatiotemporal pattern formation leads to understanding of the interesting and complex dynamics of prey-predator populations. Luckinbill [9,10] has studied the effect of dispersal on stability as well as persistence/extinction of population over a longer period of time Based on these data, works are done where the prey-predator models with spatial distribution are considered for various ecological processes [11], such as plankton patchiness [12,13,14], semiarid vegetation patterns [15], invasion by exotic species [16,17] etc. This model shows bistability since the corresponding temporal model has two stable steady-states 0 and u+ separated by an unstable steady-state u− [34] Based on this model, we are interested to study pattern formation described by the nonlocal reaction-diffusion system of prey-predator interaction with the bistable reaction kinetics of prey in the absence of predators which are specialist in nature following Holling type-II functional response. Main outcomes of this investigation are summarized in the discussion section
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