Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

and Applied Analysis 3 fj yj t, x and gj yj t, x denote the activation functions of the jth unit at time t and in space x; constant Dik ≥ 0; di yi t, x presents an amplification function; ci yi t, x is an appropriately behavior function; aij and bij denote the connection strengths of the jth unit on the ith unit, respectively; τj t corresponds to the transmission delay and satisfies 0 ≤ τj t ≤ τ ; Ji denotes the external bias on the ith unit; σij ·, ·, x is the diffusion function;X is a compact set with smooth boundary ∂X and measure mesX > 0 in R; ξi s, x is the initial boundary value; w t w1 t , . . . , wm t T is m-dimensional Brownian motion defined on a complete probability space Ω,F,P with a natural filtration {Ft}t≥0 generated by {w s : 0 ≤ s ≤ t}, where we associate Ω with the canonical space generated by all {wi t } and denote by F the associated σ-algebra generated by {w t }with the probability measure P. System 2.1 has the following matrix form: