<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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 semidiscretization method that has been implemented for computer simulations of neural networks with linear stabilizing feedback terms. The exponential convergence in the <italic>p</italic>-norm of the analogue towards the unique equilibrium point is analysed by exploiting an appropriate Lyapunov sequence and properties of an <italic>M</italic>-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.</p></abstract>

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 semidiscretization method that has been implemented for computer simulations of neural networks with linear stabilizing feedback terms. The exponential convergence in the p-norm of the analogue towards the unique equilibrium point is analysed 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 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.

Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

Department of Mathematics Faculty of Science Universiti Brunei Darussalam Gadong BE 1410 BRUNEI DARUSSALAM

Mathematical Sciences Department Faculty of Sciences United Arab Emirates University P. O. Box 17551 Al Ain UAE

Department of Mathematics & Statistics College of Science, P. O. Box 36 Sultan Qaboos University, Muscat 123 SULTANATE OF OMAN Institute of Mathematics Bulgarian Academy of Sciences Sofia BULGARIA

Tatra Mountains Mathematical Publications

A discrete-time analogue is formulated for an impulsive Cohen- -Grossberg neural network with transmission delay in a manner in which the global exponential...

Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

Publié en ligne: 12 nov. 2012

Pages: 145 - 161

DOI: https://doi.org/10.2478/v10127-009-0034-5

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

This content is open access.

Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

Publié en ligne: 12 nov. 2012

Pages: 145 - 161

DOI: https://doi.org/10.2478/v10127-009-0034-5

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

This content is open access.

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