Set-valued derivative and Lyapunov method for full-range cellular neural networks

2009 ◽  
Author(s):  
M. Di Marco ◽  
M. Forti ◽  
M. Grazzini ◽  
L. Pancioni
Keyword(s):  
Neural Networks ◽  
Lyapunov Method ◽  
Full Range ◽  
Cellular Neural Networks

Delayed Reaction–Diffusion Cellular Neural Networks of Fractional Order: Mittag–Leffler Stability and Synchronization

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Ivanka M. Stamova ◽  
Stanislav Simeonov
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Delayed Reaction

This research introduces a model of a delayed reaction–diffusion fractional neural network with time-varying delays. The Mittag–Leffler-type stability of the solutions is investigated, and new sufficient conditions are established by the use of the fractional Lyapunov method. Mittag–Leffler-type synchronization criteria are also derived. Three illustrative examples are established to exhibit the proposed sufficient conditions.

NOVEL STABILITY CRITERIA FOR DELAYED CELLULAR NEURAL NETWORKS

2003 ◽  
Vol 13 (05) ◽  
pp. 367-375 ◽  
Author(s):  
JINDE CAO ◽  
JUN WANG ◽  
XIAOFENG LIAO
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Sufficient Condition ◽  
Unique Equilibrium ◽  
Stability Criteria ◽  
Output Stability

In this paper, a new sufficient condition is given for the global asymptotic stability and global exponential output stability of a unique equilibrium points of delayed cellular neural networks (DCNNs) by using Lyapunov method. This condition imposes constraints on the feedback matrices and delayed feedback matrices of DCNNs and is independent of the delay. The obtained results extend and improve upon those in the earlier literature, and this condition is also less restrictive than those given in the earlier references. Two examples compared with the previous results in the literatures are presented and a simulation result is also given.

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