Asymmetrically coupled directed percolation systems

TL;DR

This paper introduces a coupled directed percolation model with two species, analyzing phase transitions and universality classes, revealing different behaviors in one dimension and mean field predictions, supported by simulations.

Contribution

It presents a novel asymmetric coupling model of directed percolation systems and explores its critical behavior and universality classes.

Findings

In 1D, the inhibitory coupling is irrelevant, placing the model in the unidirectionally coupled DP class.

Mean field analysis predicts the inhibitory coupling is relevant, leading to a new universality class.

Simulations on small-world networks confirm the theoretical predictions.

Abstract

We introduce a dynamical model of coupled directed percolation systems with two particle species. The two species $A$ and $B$ are coupled asymmetrically in that $A$ particles branch $B$ particles whereas $B$ particles prey on $A$ particles. This model may describe epidemic spreading controlled by reactive immunization agents. We study nonequilibrium phase transitions with focused attention to the multicritical point where both species undergo the absorbing phase transition simultaneously. In one dimension, we find that the inhibitory coupling from $B$ to $A$ is irrelevant and the model belongs to the unidirectionally coupled directed percolation universality class. On the contrary, a mean field analysis predicts that the inhibitory coupling is relevant and a new universality appears with a variable dynamic exponent. Extensive numerical simulations on small-world networks confirm our predictions.