Numerical investigation and factor analysis of the spatial-temporal multi-species competition problem

TL;DR

This paper numerically investigates a multi-species competition model using finite volume methods, analyzing the effects of diffusion, initial conditions, and parameter variability on system stability and survival outcomes.

Contribution

It introduces a numerical approach with factor analysis to study the impact of diffusion and parameter uncertainty in multi-species competition models.

Findings

Diffusion significantly influences survival scenarios.

Random initial conditions affect time to equilibrium.

Parameter variability impacts system stability.

Abstract

In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time approximation for the numerical solution of the model with corresponding boundary and initial conditions. To understand the effect of the diffusion to solution in one and two-dimensional formulations, we present numerical results for several cases of the parameters related to the survival scenarios. The random initial conditions' effect on the time to reach equilibrium is investigated. The influence of diffusion on the survival scenarios is presented. In real-world problems, values of the parameters are usually unknown and vary in some range. In order to evaluate the impact of parameters on the system stability, we simulate a spatial-temporal model with random parameters and perform factor analysis for two and three-species competition models.