Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species

TL;DR

This study investigates how changing invasion rates in spatial cyclic predator-prey models with four or six species affects their dynamics, revealing a phase transition from self-organizing patterns to frozen states.

Contribution

It demonstrates the existence of a threshold invasion rate deviation that triggers a continuous phase transition in multi-species cyclic predator-prey models.

Findings

Self-organizing patterns persist within a threshold deviation.

Beyond the threshold, the system transitions to a frozen distribution.

Phase transition is continuous and depends on invasion rate deviations.

Abstract

Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion rate(s) from a uniform value does not exceed a threshold value. For larger deviations the system exhibits a continuous phase transition into a frozen distribution of odd (or even) label species.