Critical Behavior and Threshold of Coexistence of a Predator–prey Stochastic Model in a 2d Lattice

Abstract

We investigate the critical behavior of a stochastic lattice model describing a predator–prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Absorbing phase transition in a parity-conserving particle process on a Sierpinski carpet fractal

“…From p c = 1 we obtain γ , /Zν ⊥ = 0.85 (2). Comparing this result with that one of γ , /Zν ⊥ = 2/D w = 0.91 (6), they seem to be coincidental within error bars. For this calculation, we used hyperscaling relation γ , = ν ⊥ (2 − η) and η = 0 once it was not calculated in [16].…”

“…We report the estimated critical exponent γ , /Zν ⊥ = 0.85 (2) in table 1 where we used the value p c = 1. We compare this result with the one of hyperscaling relation γ , = (2 − η)ν ⊥ calcul ation and with η = 0 we have γ , /Zν ⊥ = 2/D w = 0.91 (6) and they seem to coincide within error bars. This was not computed in [16].…”

“…The study of critical properties of diusive individuals infecting a static population was done in [5]. In works [5,6] some of us analyzed the critical behavior of one and two dimensional models. In [6] we considered a model of an epidemic process in a population of diusive individuals, a diusion-limited reaction model of two interacting species simulating the dynamics of an epidemic process.…”

“…In works [5,6] some of us analyzed the critical behavior of one and two dimensional models. In [6] we considered a model of an epidemic process in a population of diusive individuals, a diusion-limited reaction model of two interacting species simulating the dynamics of an epidemic process. On the substrate of the Sierpinski carpet, we considered in [7] a model for a stochastic predator-prey system presenting an active state, where both species may coexist and an absorbing state with extinction of one of the species.…”

Spatial dynamics in a predator-prey model with herd behavior

“…2,20,21 Recently, many research scholars pointed out that spatial mathematical model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal population dynamics. [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] In their researches, reactiondiffusion (RD) equations have been widely used to describe the spatiotemporal dynamics. Since Turing 37 first proposed RD theory to describe the range of spatial patterns observed in the developing embryo, RD models have been studied extensively to explain pattern formation in many areas.…”