Stochastic modifications of Lotka–Volterra models with non-antagonistic interactions

Stochastic modifications of two-dimensional and three-dimensional dynamic models are constructed taking into account competitive and symbiotic interactions. The transition from deterministic systems to stochastic systems is performed using a symbolic computing algorithm developed on the basis of the normal approximation method. Deterministic systems of differential equations with respect to first- and second-order moments are obtained. Taking into account non-antagonistic interactions and random perturbations related to nonparametric white noise, the effects of stochastisation are analyzed and computer modeling of the dynamics of mathematical expectations, variances and covariances is carried out. Solution trajectories are constructed for various sets of parameters. The results can be used in modeling processes described using stochastic generalizations of Lotka–Volterra systems.