The authors discuss the th moment exponential stability of zero solution to the generalized stochastically perturbed neural network model with time-varying defined by the state equation:
where is the transmission delay and denotes an dimensional Brownian motion on a complete probability space. The following assumptions are given:
(1) is a differentiable function with a constant such that ,
(2) satisfy the Lipschitz condition,
It is known that under the above conditions there exists a unique global solution to the above state equation. Thus, the authors discuss the th moment exponential stability of zero solution. The main theorem is the following.
Theorem. If then the zero solution to the above system is th moment exponentially stable.
This theorem is a generalization of the theorem on exponential stability proven by L. Wan and J. Sun [Phys. Lett., 342, No. 4, 331–340 (2005; Zbl 1222.93200)].
The authors also give two numerical examples.