Exponential stability of continuous-time and discrete-time cellular neural networks with delays

2003 ◽  
Vol 135 (1) ◽  
pp. 17-38 ◽  
Author(s):  
S. Mohamad ◽  
K. Gopalsamy
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Continuous Time ◽  
Cellular Neural Networks

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

2009 ◽  
Vol 43 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Sannay Mohamad ◽  
Haydar Akça ◽  
Valéry Covachev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Continuous Time ◽  
Global Exponential Stability ◽  
Exponential Convergence ◽  
Unique Equilibrium ◽  
Transmission Delays

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.

A NOVEL GLOBAL EXPONENTIAL STABILITY RESULT FOR DISCRETE-TIME CELLULAR NEURAL NETWORKS WITH VARIABLE DELAYS

2006 ◽  
Vol 16 (06) ◽  
pp. 467-472 ◽  
Author(s):  
QIANG ZHANG ◽  
XIAOPENG WEI ◽  
JIN XU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Stability Condition ◽  
Global Exponential Stability ◽  
Stability Result ◽  
Cellular Neural Networks ◽  
Unique Equilibrium ◽  
Variable Delays

Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here.

DYNAMICS FOR DISCRETE-TIME CELLULAR NEURAL NETWORKS

2004 ◽  
Vol 14 (08) ◽  
pp. 2667-2687 ◽  
Author(s):  
SHYAN-SHIOU CHEN ◽  
CHIH-WEN SHIH
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Energy Function ◽  
Continuous Time ◽  
Chaotic Dynamics ◽  
Homoclinic Orbits ◽  
Cellular Neural Networks ◽  
Attracting Set ◽  
Transversal Homoclinic Orbits

This presentation investigates the dynamics of discrete-time cellular neural networks (DT-CNN). In contrast to classical neural networks that are mostly gradient-like systems, DT-CNN possesses both complete stability and chaotic behaviors as different parameters are considered. An energy-like function which decreases along orbits of DT-CNN as well as the existence of a globally attracting set are derived. Complete stability can then be concluded, with further analysis on the sets on which the energy function is constant. The formations of saturated stationary patterns for DT-CNN are shown to be analogous to the ones in continuous-time CNN. Thus, DT-CNN shares similar properties with continuous-time CNN. By confirming the existence of snap-back repellers, hence transversal homoclinic orbits, we also conclude that DT-CNN with certain parameters exhibits chaotic dynamics, according to the theorem by Marotto.

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