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Discrete-Time Analogues of Impulsive Cohen-Grossberg Neural Networks with Transmission Delays

Sannay Mohamad, Haydar Akca, Valery Covachev


A discrete-time analogue is formulated for an impulsive Cohen-Grossberg neural network with transmission delay in a manner in which the global exponential stability characterisitics of a unique equilibrium point of the network are preserved. The formulation is based on extending the existing semi-discretization method that has been implemented for computer simulations of neural networks with linear stabilizing feedback terms. The exponential convergence in the __norm of the analogue towards the unique equilibrium point is analysed by exploiting an appropriate Lyapunov sequence and properties of an __matrix. The main result yields a Lyapunov exponent that involves the magnitude and frequency of the impulses. One can use the result for deriving the exponential stability of non-impulsive discrete-time neural networks, and also for simulating the exponential stability of impulsive and non-impulsive continuous-time networks.


Cohen-Grossberg neural networks, delays, discrete-time analogues, Lyapunov exponents.

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