About Stability of One System of Stochastic Difference Equations with Exponential Nonlinearity

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 the equilibrium and numerical simulation of the solution of the considered system of stochastic difference equations. The proposed research method can be applied to nonlinear systems of higher dimension and with other types of high-order nonlinearity, both for stochastic difference equations and for stochastic differential equations with delay.