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In this work, we consider the spatial-temporal multi-species competitionmodel. A mathematical model is described by a coupled system of nonlineardiffusion-reaction equations. We use a finite volume approximation withsemi-implicit time approximation for the numerical solution of the model withcorresponding boundary and initial conditions. To understand the effect of thediffusion to solution in one and two-dimensional formulations, we presentnumerical results for several cases of the parameters related to the survivalscenarios. The random initial conditions' effect on the time to reachequilibrium is investigated. The influence of diffusion on the survivalscenarios is presented. In real-world problems, values of the parameters areusually unknown and vary in some range. In order to evaluate the impact ofparameters on the system stability, we simulate a spatial-temporal model withrandom parameters and perform factor analysis for two and three-speciescompetition models.

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