Cross-diffusion-driven instability in an interacting species model with prey refuge

Lakshmi Narayan Guin, Salih Djilali and Santabrata Chakravarty

Chaos, Solitons & Fractals, 2021, vol. 153, issue P1

Abstract: The present study appertains to a reaction-diffusion system embracing two-dimensional continuous Beddington-DeAngelis predator-prey model incorporating intra-specific competition among predators and prey refuge in proportion to both the species as well. The existence of all conceivable ecologically significant equilibria is explored and consequently the diffusion-driven instability around the coexistence equilibrium position is reviewed. Numerical simulation with zero-flux boundary conditions discloses that the system under consideration experiences the occurrence of diffusion-driven instability. The dynamical system in Turing space emerges further to get influenced by prey refuge while it unveils diffusion controlled spatiotemporal pattern formation namely, growth of spots, stripe-spot mixtures, stripes, labyrinthine, stripe-hole mixtures and holes reproduction. The quantitative analysis reveals that the interaction of both self- and cross-diffusion plays a significant role on the pattern formation of the present system in a way to enrich the pattern at a greater height.

Keywords: Non-linear differential equations; Nonlinear stabilities; Bifurcation problems; Diffusion-driven instability; Spatial patterns (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008559

DOI: 10.1016/j.chaos.2021.111501

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