Stochastic analysis of predator-prey type ecosystems

A stochastic model for the predator-prey type ecosystems in a random environment is proposed and investigated. The model is a variation of the Lotka-Volterra type with an additional self-competition mechanism within the prey population. Two different situations are considered: (1) saturation of predators, and (2) competition among predators. Changes in the birth rate of the preys and the death rate of the predators are modeled as random processes. The stochastic averaging procedure of Stratonovich and Khasminskii is applied to obtain the probability distribution of the system state variables at the state of statistical stationarity. Asymptotic behaviors of the system are also investigated. Effects on the ecosystem behaviors are evaluated of (1) prey self-competition, (2) predator saturation and predator competition, (3) random variation in the prey birth rate, and (4) random variation in the predator death rate.