Modern Stochastics: Theory and Applications

A system of two nonlinear delay differential equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on the both variables of the system. The stability in probability of the zero and nonzero equilibria 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 differential equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, both for delay differential equations and for difference equations.