A discrete-time analogue is formulated for an impulsive Cohen-Grossberg neural network withtransmission delay in a manner in which the global exponential stability characterisitics ofa unique equilibrium point of the network are preserved. The formulation is based onextending the existing semi-discretization method that has been implemented for computersimulations of neural networks with linear stabilizing feedback terms. The exponentialconvergence in the $p-$norm of the analogue towards the unique equilibrium point isanalysed by exploiting an appropriate Lyapunov sequence and properties of an $M-$matrix.The main result yields a Lyapunov exponent that involves the magnitude and frequency ofthe impulses. One can use the result for deriving the exponential stability of non-impulsivediscrete-time neural networks, and also for simulating the exponential stability ofimpulsive and non-impulsive continuous-time networks.
@article{24,
title = {Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses},
journal = {Tatra Mountains Mathematical Publications},
volume = {43},
year = {2009},
doi = {10.2478/tatra.v43i0.24},
language = {EN},
url = {http://dml.mathdoc.fr/item/24}
}
Mohamad, Sannay; Akça, Haydar; Covachev, Valery. Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses. Tatra Mountains Mathematical Publications, Tome 43 (2009) . doi : 10.2478/tatra.v43i0.24. http://gdmltest.u-ga.fr/item/24/