Application of stochastic averaging to non-linear ecosystems

Stochastic models for the prey–predator type ecosystems in a random environment are proposed and investigated. They are the stochastic versions of the classical Lotka–Volterra model, the predator-saturation model, and the time-delay model. Variations in the birth rate of the preys and the death rate of the predators are modeled as random processes. For the three stochastic models, the stochastic averaging procedure of Stratonovich and Khasminskii is applied to obtain the probability distributions of the prey and predator populations at the state of statistical stationarity. Effects of different system parameters on the ecosystem behaviors are evaluated. The analytical results are substantiated by results obtained from Monte Carlo simulations.