On the existence of stable equilibrium points in cellular neural networks

2003 ◽  
Author(s):  
M. Gilli ◽  
M. Biey ◽  
P.P. Civalleri
Keyword(s):  
Neural Networks ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Cellular Neural Networks

ON THE EXISTENCE OF STABLE EQUILIBRIUM POINTS IN CELLULAR NEURAL NETWORKS

2003 ◽  
Vol 12 (04) ◽  
pp. 461-471 ◽  
Author(s):  
NEYIR OZCAN ◽  
SABRI ARIK ◽  
VEDAT TAVSANOGLU
Keyword(s):  
Neural Networks ◽  
Stable Equilibrium ◽  
Opposite Sign ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Saturation Region ◽  
New Criteria ◽  
Special Classes

This paper presents new criteria for the existence of stable equilibrium points in the total saturation region for cellular neural networks (CNNs). It is shown that the results obtained can be used to derive some complete stability conditions for some special classes of CNNs such as positive cell-linking CNNs, opposite-sign CNNs and dominant-template CNNs. Our results are also compared with the previous results derived in the literature for the existence of stable equilibrium points for CNNs.

A New Approach for Estimating the Attraction Domain for Hopfield-Type Neural Networks

2009 ◽  
Vol 21 (1) ◽  
pp. 101-120 ◽  
Author(s):  
Dequan Jin ◽  
Jigen Peng
Keyword(s):  
Neural Networks ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Numerical Results ◽  
New Method ◽  
Attraction Domain ◽  
Network System ◽  
Asymptotically Stable ◽  
New Approach

In this letter, using methods proposed by E. Kaslik, St. Balint, and their colleagues, we develop a new method, expansion approach, for estimating the attraction domain of asymptotically stable equilibrium points of Hopfield-type neural networks. We prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient. The numerical results that obtained in the application examples, including the network system considered by E. Kaslik, L. Brăescu, and St. Balint, indicate that the proposed approach is able to achieve better attraction domain estimation.

Analysis on equilibrium points of cells in cellular neural networks described using cloning templates

2012 ◽  
Vol 89 ◽  
pp. 106-113 ◽  
Author(s):  
Qi Han ◽  
Xiaofeng Liao ◽  
Tengfei Weng ◽  
Chuandong Li ◽  
Hongyu Huang
Keyword(s):  
Neural Networks ◽  
Equilibrium Points ◽  
Cellular Neural Networks

STRUCTURALLY STABLE TWO-CELL CELLULAR NEURAL NETWORKS

2004 ◽  
Vol 14 (08) ◽  
pp. 2579-2653 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Neural Networks ◽  
Phase Portrait ◽  
Limit Cycles ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Global Phase Portrait ◽  
Structurally Stable

The global phase portrait of structurally stable two-cell cellular neural networks is studied. The configuration of equilibrium points, the number of limit cycles and their locations are investigated systematically.

Bifurcation and Chaos in Noninteger Order Cellular Neural Networks

1998 ◽  
Vol 08 (07) ◽  
pp. 1527-1539 ◽  
Author(s):  
P. Arena ◽  
R. Caponetto ◽  
L. Fortuna ◽  
D. Porto
Keyword(s):  
Neural Networks ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Cell System ◽  
Bifurcation And Chaos ◽  
Chaotic Motions ◽  
First Order ◽  
New Class ◽  
Onset Of Chaos ◽  
Coupling Parameters

In this paper a new class of Cellular Neural Networks (CNNs) is introduced. The peculiarity of the new CNN model consists in replacing the traditional first order cell with a noninteger order one. The introduction of fractional order cells, with a suitable choice of the coupling parameters, leads to the onset of chaos in a two-cell system of a total order of less than three. A theoretical approach, based on the interaction between equilibrium points and limit cycles, is used to discover chaotic motions in fractional CNNs.

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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