Abstract
Abstract A reaction–diffusion system governing the prey–predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.
Highlights
Ecological systems are characterized by the interaction between species and their natural environment
A reaction–diffusion system governing the prey–predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation
It has turned out that predator–prey systems can show different dynamical behaviors depending on the value of model parameters
Summary
Ecological systems are characterized by the interaction between species and their natural environment. In particular it has been shown that reaction–diffusion systems are capable of self organized pattern formation These spatial patterns arise not from inhomogeneity of initial or boundary conditions, but purely from the dynamics of the system, i.e. from the interaction of nonlinear reactions of growth processes and diffusion (as shown already by Turing [14]). Linear stability analysis has been performed and conditions guaranteeing that a biological meaningful equilibrium, stable in the absence of diffusion, becomes unstable in the presence of diffusion (Turing instability) have been found For this model, we showed some numerical simulations which highlight the impact of different choices for the diffusion coefficients on the dynamics of the two populations and in particular we explored the Turing patterns formation.
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