Reaction-diffusion stochastic lattice model for a predator-prey system

Rodrigues, Áttila Leães; Tomé, Tânia

doi:10.1590/s0103-97332008000100017

Cited by 9 publications

(7 citation statements)

References 37 publications

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“…Our approach is the one based on stochastic spatially structured models. In the last years, a great number of works have shown the relevance of this kind of approach to describe biological population problems [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. We focus on the stochastic lattice model for a susceptible-infected-immunized system introduced by Satulovsky and Tomé [24,25].…”

Section: Introductionmentioning

confidence: 99%

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Argolo

Quintino

Gleria

et al. 2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe investigate the critical behavior of a stochastic lattice model describing a General Epidemic Process. By means of a Monte Carlo procedure, we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization. A finite size scaling analysis is employed to determine the critical point as well as some critical exponents. We show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point. Precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations. Our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class. We also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters.

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Section: Introductionmentioning

confidence: 99%

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Argolo

Quintino

Gleria

et al. 2011

Physica A: Statistical Mechanics and its Applications

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“…For example, the majority-vote model exhibits a similar phase transition between a ferromagnetic phase (ordered) and a paramagnetic phase (disordered), even without any spontaneous opinion change, with the critical parameter given by ω t = 0.135 in a pair mean-field approximation on square lattices (denoted here by the same notation as that used before for the sake of clarity) [12]. Other models describing spreading diseases and prey-predator biological populations can also be put in the same context of comparisons and display a phase transition between an active state and an absorbing state on square lattices with the pair mean-field critical parameter respectively equal to ω t = 0.379 [13,14] and ω t = 0.235 [15], showing results closer to the Sznajd model than the majority-vote model. More comparisons with other important models are made in Table III [16].…”

Section: Critical Behavior Of the Modelmentioning

confidence: 99%

Mean-field approximation for the Sznajd model in complex networks

et al. 2015

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This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.

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“…The common point between the abovementioned approaches is that they are Eulerian and deterministic and known as the mean-field approach. There is still some stochastic formulations studied in [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A Predator-Prey Model from Collective Dynamics and Self-Propelled Particles Approach

Yaya

2022

Preprint

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The definition and description of the dynamics of predator-prey system consists in one of the fundamental problems of the population biology. Since 1925, several models have been introduced. Although they are highly effective, most of them neglect certain relevant criteria such as the spatial and temporal distribution of the studied species. We introduced these criteria by coupling two models designed initially for collective dynamics. The first is for predators mobility, a Vicsek type model and the second is a Brownian Particle (BP) model for prey. We observed, as naturally in the classical models, periodic cycles of the density of predators and prey. In this case, the period of oscillations depends relatively on the collective dynamics parameters.

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Reaction-diffusion stochastic lattice model for a predator-prey system

Cited by 9 publications

References 37 publications

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Mean-field approximation for the Sznajd model in complex networks

A Predator-Prey Model from Collective Dynamics and Self-Propelled Particles Approach

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