Numerical Investigation and Factor Analysis of Two-Species Spatial-Temporal Competition System after Catastrophic Events

Abstract

The interaction of species in an ecological community can be described by coupled system partial differential equations. To analyze the problem numerically, we construct a discrete system using finite volume approximation by space with semi-implicit time approximation to decouple a system. We first simulate the converges of the system to the final equilibrium state for given parameters (reproductive rate, competition rate, and diffusion rate), boundaries, and initial conditions of population density. Then, we apply catastrophic events on a given geographic position with given catastrophic sizes to calculate the restoration time and final population densities for the system. After that, we investigate the impact of the parameters on the equilibrium population density and restoration time after catastrophe by gradually releasing the hold of different parameters. Finally, we generate data sets by solutions of a two-species competition model with random parameters and perform factor analysis to determine the main factors that affect the restoration time and final population density after catastrophic events.