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A system of two nonlinear difference equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on all variables of the system. The stability in probability of a positive equilibrium of the system is studied via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic difference equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, for both difference equations and for delay differential equations.
Leonid Shaikhet (Thu,) studied this question.