Segregation process and phase transition in cyclic predator-prey models with even number of species

TL;DR

This paper investigates how spatial cyclic predator-prey models with an even number of species undergo segregation and phase transitions, revealing the conditions under which species form alliances or domains on a lattice.

Contribution

It introduces a detailed analysis of segregation and phase transition phenomena in cyclic predator-prey models with even species counts, using Monte Carlo simulations.

Findings

Segregation occurs at low exchange probability X.

Domain formation by species alliances at high X.

Blocking of segregation in certain parameter ranges for n=8.

Abstract

We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of a square lattice. The evolution of spatial distribution is governed by iteration of two elementary processes on neighboring sites chosen randomly: if the sites are occupied by a predator-prey pair then the predator invades the prey's site; otherwise the species exchange their site with a probability $X$. For low $X$ values a self-organizing pattern is maintained by cyclic invasions. If $X$ exceeds a threshold value then two types of domains grow up that formed by the odd and even label species, respectively. Monte Carlo simulations indicate the blocking of this segregation process within a range of X for n=8.