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.

Stability of Equilibrium Points in Cellular Neural Networks with Negative Slope Activation Function

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Qi Han ◽  
Qian Xiong ◽  
Chao Liu ◽  
Jun Peng ◽  
Lepeng Song ◽  
...  
Keyword(s):  
Neural Networks ◽  
Equilibrium Points ◽  
Activation Function ◽  
Cellular Neural Networks ◽  
Negative Slope ◽  
Stability Of Equilibrium

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.

Analysis of Complete Stability for Discrete-Time Cellular Neural Networks with Piecewise Linear Output Functions

2009 ◽  
Vol 21 (5) ◽  
pp. 1434-1458 ◽  
Author(s):  
Xuemei Li
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Multiple Equilibrium ◽  
Small Perturbations ◽  
Feedback Matrix ◽  
Multiple Equilibrium Points ◽  
Stability Results

This letter discusses the complete stability of discrete-time cellular neural networks with piecewise linear output functions. Under the assumption of certain symmetry on the feedback matrix, a sufficient condition of complete stability is derived by finite trajectory length. Because the symmetric conditions are not robust, the complete stability of networks may be lost under sufficiently small perturbations. The robust conditions of complete stability are also given for discrete-time cellular neural networks with multiple equilibrium points and a unique equilibrium point. These complete stability results are robust and available.

Analysis on Cellular Neural Networks with Negative Slope Activation Function

2013 ◽  
Vol 427-429 ◽  
pp. 2493-2496
Author(s):  
Qi Han ◽  
Qian Xiong ◽  
Chao Liu ◽  
Jun Peng ◽  
Le Peng Song ◽  
...  
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Activation Function ◽  
Cellular Neural Networks ◽  
Negative Slope ◽  
The Relationship ◽  
Inputs And Outputs

In the paper, the region of the number of equilibrium points of every cell in cellular neural networks with negative slope activation function is considered by the relationship between parameters of cellular neural networks. Some conditions are obtained by using the relationship among connection weights. Depending on these sufficient conditions, inputs and outputs of a CNN, the regions of the values of parameters can be obtained. Some numerical simulations are presented to support the effectiveness of the theoretical analysis.

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