On a non-standard two-species stochastic competing system and a related degenerate parabolic equation

Abstract

We propose and analyse a new stochastic competing two-species population dynamics model. Competing algae population dynamics in river environment, important engineering problems, motivate this model. It is a system of stochastic differential equations (SDEs) and has a characteristic that the two populations are competing with each other through the environmental capacities. Unique existence of the uniformly bounded strong solution is proven and an attractor is identified. The Kolmogorov backward equation associated with the population dynamics is formulated and its unique solvability in a Banach space with a weighted norm is discussed. Our mathematical analysis results can be effectively utilized for a base-stone of modelling, analysis, and control of the competing population dynamics.