On hybrid competitive Lotka–Volterra ecosystems Original Research Article

This paper is concerned with competitive Lotka–Volterra model in random environments. It uses regime-switching diffusion to model the dynamic of population sizes of n different species in a ecosystem subject to the random changes of the external environment. We show that the positive solution of the associated stochastic differential equation does not explode in finite time with probability 1. Moreover, we demonstrate that the solution is stochastically bounded, continuous, and has finite moments. Furthermore, we obtain certain asymptotic results regarding large time behavior and present some numerical experimental results.