Stochastic model of dynamics of biological community in conditions of consumption by individuals of harmful food resources
Pertsev N.V., Loginov K.K.
Omsk Branch Institute of Mathematics SB RAS, Omsk, Russia
Abstract. The stochastic model describing dynamics of biological community in conditions of consumption by individuals of food resources, containing harmful substances is presented. For construction the model we used stochastic analogue of Lotka-Volterra model in the form of multivariate nonlinear birth and death process, added by the differential equations for quantity of food resources. Decrease in number of populations of community is described by death of individuals not only due to their competition and a self-capping, but also due to consumption of the food resources containing harmful substances. The recurrent equations specifying rules of variation of number of populations and quantity of food resources in an inhabitancy of individuals are constructed. On the basis of Monte-Carlo technique the algorithm for simulation the dynamics of number of populations and quantities of food resources is developed. Results of computing experiments on studying dynamics of two competing populations which individuals consume the complete set from four food resources containing two harmful substances are resulted.
Key words: stochastic model, nonlinear birth and death process, Lotka-Volterra model , the food resources, harmful substances, Monte-Carlo technique, computing experiment.