# Front propagation and effect of memory in stochastic desertification models with an absorbing state

## TL;DR

This paper investigates how stochastic effects influence desertification transitions in dryland ecosystems, revealing that noise can induce continuous transitions and affect front propagation, with implications for ecosystem resilience.

## Contribution

It presents a numerical analysis of a stochastic desertification model, highlighting the role of memory and stochasticity in transition dynamics and front propagation behavior.

## Key findings

- Stochasticity enables propagating fronts only during active invasion.
- Transient front propagation occurs before global collapse in extinction phase.
- Seed banks increase vegetation robustness but do not change the transition class.

## Abstract

Desertification in dryland ecosystems is considered to be a major environmental threat that may lead to devastating consequences. The concern increases when the system admits two alternative steady states and the transition is abrupt and irreversible (catastrophic shift). However, recent studies show that the inherent stochasticity of the birth-death process, when superimposed on the presence of an absorbing state, may lead to a continuous (second order) transition even if the deterministic dynamics supports a catastrophic transition. Following these works we present here a numerical study of a one-dimensional stochastic desertification model, where the deterministic predictions are confronted with the observed dynamics. Our results suggest that a stochastic spatial system allows for a propagating front only when its active phase invades the inactive (desert) one. In the extinction phase one observes transient front propagation followed by a global collapse. In the presence of a seed bank the vegetation state is shown to be more robust against demographic stochasticity, but the transition in that case still belongs to the directed percolation equivalence class.