Stochastic Modelling for Dynamics of Interacting Populations

The paper deals with a mathematical model for two interacting populations. Under the assumption of fast stochastic contacting of populations, we derive stochastic Poisson-type differential equations with a small parameter and propose an approximative algorithm for quantitative analysis of population dynamics that consists of two steps. First, we derive an ordinary differential equation for mean value of each population growth and analyse the average asymptotic population behaviour. Then, applying diffusion approximation procedure, we derive a stochastic Ito differential equation for small random deviations on the average motion in a form of a linear non-homogeneous Ito stochastic differential equation and analyse the probabilistic characteristics of the Gaussian process given by this equation.