Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

and Applied Analysis 3 Theneuron activation functions,g p (y p (⋅)) (p = 1, . . . , n), are assumed to be nondecreasing, bounded, and globally Lipschitz; that is, l − p ≤ g p (ξ p ) − g p (ξ q ) ξ p − ξ q ≤ l + p , ∀ξ p , ξ q ∈ R, ξ p ̸ = ξ q , (5) where l− p and l+ p are constant values. For simplicity, in stability analysis of the network (1), the equilibrium point y∗ = [y∗ 1 , . . . , y ∗ n ] T is shifted to the origin by the utilization of the transformationy(⋅) = y(⋅)−y, which leads the network (1) to the following form: y (k + 1) = (A + ΔA) y (k − τ) + (W 1 + ΔW 1 ) g (y (k)) + (W 2 + ΔW 2 ) g (y (k − h (k))) , (6) where y(⋅) = [y 1 (⋅), . . . , y n (⋅)] T ∈ Rn is the state vector of the transformed network, and g(y(⋅)) = [g 1 (y 1 (⋅)), . . . , g n (y n (⋅))] T is the transformed neuron activation function vector with g q (y q (⋅)) = g q (y q (⋅) + y ∗ q ) − g q (y ∗ q ) (q = 1, . . . , n) satisfies, from (5), l− p ≤ g p (ξ p )/ξ p ≤ l + p , ∀ξ p ̸ = 0, which is equivalent to [g p (y p (k)) − l − p y p (k)] [g p (y p (k)) − l + p y p (k)] ≤ 0. (7) In this paper, a model of coupled stochastic discretetime neural networks with interval time-varying delays in network coupling, leakage delay, and parameter uncertainties is considered as y i (k + 1) = (A + ΔA) y i (k − τ) + (W 1 + ΔW 1 ) g (y i (k)) + (W 2 + ΔW 2 ) g (y i (k − h (k)))