Dynamic Preservation for a Class of Semi-Discrete Recurrent Neural Networks

The dynamic preservation in discrete simulations of the recurrent neural networks (RNNs) with discrete and infinite distributive asynchronous time delays is addressed. Firstly, we formulate the corresponding discrete-time model by semi-discrete technique. Secondly, we derive several mild algebra conditions to guarantee that the discussed discrete-time system is the global exponential stability in Lyapunov sense. It is shown analytically that the discrete-time technique is able to maintain the uniqueness of equilibrium point and its dynamic behavior of the continuous-time model under the same conditions. Meanwhile, we also show that there exists some degree of deviation in the spatial position among the equilibrium points of the continuous-time model and its discrete-time analogue due to the rounding error. Finally, we verify the validity of the main obtained results by comparing one continuous-time numerical example with its discrete-time counterpart.