Absorbing Phase Transition in a Four State Predator Prey Model in One Dimension

TL;DR

This study investigates a one-dimensional predator-prey model exhibiting a non-equilibrium phase transition into an absorbing state, with unique critical behavior distinct from the Directed Percolation universality class.

Contribution

It introduces a four-state predator-prey model with novel interactions and demonstrates a new type of absorbing phase transition with distinct critical exponents.

Findings

System exhibits a non-equilibrium phase transition to an absorbing state.

Critical exponents differ from Directed Percolation universality class.

Robustness of critical behavior against explicit diffusion.

Abstract

The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator, or occupied by a single prey, or by both. Along with the pairwise death of predators and growth of preys, we introduce an interaction where the predators can eat one of the neighboring prey and reproduce a new predator there instantly. The model shows a non-equilibrium phase transition into a unusual absorbing state where predators are absent and the lattice is fully occupied by preys. The critical exponents of the system are found to be different from that of the Directed Percolation universality class and they are robust against addition of explicit diffusion.