Dynamics of a diffusive competitive model on a periodically evolving domain

TL;DR

This study investigates how periodic habitat evolution influences the dynamics of a two-species competitive model with diffusion, revealing that faster habitat evolution promotes species persistence.

Contribution

It introduces a Lagrangian transformation method to analyze the model on evolving domains and establishes thresholds for species survival based on habitat evolution rates.

Findings

Faster habitat evolution enhances species persistence.

Both species survive or vanish depending on the evolution rate.

Numerical simulations confirm theoretical predictions.

Abstract

In this paper, we are concerned with a two-species competitive model with diffusive terms on a periodically evolving domain and study the impact of the spatial periodic evolution on the dynamics of the model. The Lagrangian transformation approach is adopted to convert the model from a changing domain to a fixed one with the assumption that the evolution of habitat is uniform and isotropic. The ecological reproduction indexes of the linearized model are given as thresholds to reveal the dynamic behaviour of the competitive model by discussing the relations between the initial boundary value problem and its corresponding periodic problem. Our theoretical results show that a lager evolving rate benefits the persistence of competitive populations for both sides in the long run. Numerical experiments illustrate that two competitive species, one of which survive and the other vanish on a fixed domain, both survive on a domain with a large evolving rate and both vanish on a domain with a small evolving rate.