Construction of algorithms for the study of multidimensional stochastic Lotka – Volterra systems using the normal approximation method

The relevance of the study of multidimensional stochastic Lotka – Volterra systems is related to the possibilities of using the results to analyze the effect of random disturbances on population dynamics in environmental problems, as well as on the dynamics of phase variables in problems of chemical kinetics, physics, epidemiology, demography and other fields. The article considers stochastic modifications of multidimensional Lotka – Volterra systems constructed taking into account random perturbations related to nonparametric white noise. An algorithm for the transition from stochastic modification to a system of ordinary differential equations with respect to probabilistic moments of the first and second order is proposed. The algorithm is based on the application of the recurrence relations of the normal approximation method in which the approximation of unknown distributions by a normal distribution is performed taking into account the transition to a deterministic system of a higher dimension compared to the dimension of the original stochastic system. The applicability of the algorithm is demonstrated by using examples of studies of the "predator – prey" model with intraspecific competition and the "competitor – competitor – migration area" model. The results can be used in modeling dynamical systems with polynomial-type nonlinearities, taking into account random perturbations, as well as in constructing nonlinear stochastic filters.