# Critical and quasicritical behavior in a three-species dynamical model of semi-directed percolation

## TL;DR

This paper studies a three-species model exhibiting phase transitions similar to directed percolation, analyzing critical behavior, the impact of spontaneous activity, and identifying quasi-critical phenomena with two pseudo-thresholds.

## Contribution

It introduces a three-species dynamical model that belongs to the directed percolation universality class and explores the effects of spontaneous activity on critical behavior.

## Key findings

- Model belongs to directed percolation universality class
- Spontaneous activity destroys usual critical behavior
- Presence of two pseudo-thresholds with distinct scale-free properties

## Abstract

We investigate a one-dimensional three-species dynamical model whose dynamics naturally generate the semi-directed percolation cluster in time and show a non-equilibrium absorbing state phase transition from an active to inactive state. The critical threshold and exponents associated with the dynamic process are determined using Monte Carlo simulations. Critical behavior observed shows that the model belongs to the directed percolation (DP) universality class. Further, we consider the effect of spontaneous activity generation in the dynamical model. While, as expected, this destroys the usual critical behaviour, we find that the dynamic susceptibility shows a maximum at a specific value of the control parameter, indicating a quasi-critical behaviour, similar to the findings in the case of DP models and DP-inspired models of neuronal activity with spontaneous activity generation. Interestingly, in the presence of spontaneous activity, we find that spatial and temporal correlations exhibit power-law decays at a value of the control parameter different from the pseudo-threshold corresponding to the peak of the dynamic susceptibility, indicating that there are two pseudo-thresholds in such a case, one where the response function is maximum and another where the spatial and temporal correlations show scale-free behaviour.