Necessary and sufficient conditions for one-dimensional discrete-time binary cellular neural network with nonsymmetric connections to be stable

2004 ◽  
Author(s):  
H. Hara ◽  
N. Takahashi ◽  
T. Nishi
Keyword(s):  
Neural Network ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Cellular Neural Network ◽  
Necessary And Sufficient Conditions ◽  
One Dimensional ◽  
Necessary And Sufficient

THE MOSAIC PATTERNS OF CNN WITH SYMMETRIC FEEDBACK TEMPLATE

2008 ◽  
Vol 18 (02) ◽  
pp. 375-390 ◽  
Author(s):  
YUNQUAN KE
Keyword(s):  
Neural Network ◽  
Parameter Space ◽  
Sufficient Conditions ◽  
Cellular Neural Network ◽  
Necessary And Sufficient Conditions ◽  
Two Dimensional ◽  
Geometric Methods ◽  
Variable Substitution ◽  
Necessary And Sufficient

In this paper, the mosaic patterns of the two-dimensional cellular neural network (CNN) with symmetric feedback template are investigated. For our CNN system, the parameter space is constructed by the output synaptic weights and the threshold, and it is partitioned into finitely many regions through geometric methods and variable substitution. Fixing the output synaptic weights and the threshold in some regions, we give the necessary and sufficient conditions to all mosaic patterns of the CNN systems.

GENERALIZED DECIMATION INVARIANT SEQUENCES IN DIMENSION N

2002 ◽  
Vol 12 (04) ◽  
pp. 709-737 ◽  
Author(s):  
A. BARBÉ ◽  
F. VON HAESELER
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
One Dimensional ◽  
Necessary And Sufficient

We generalize the concept of one-dimensional decimation invariant sequences, i.e. sequences which are invariant under a specific rescaling, to dimension N. After discussing the elementary properties of decimation-invariant sequences, we focus our interest on their periodicity. Necessary and sufficient conditions for the existence of periodic decimation invariant sequences are presented.

scholarly journals Positive 2D Discrete-Time Linear Lyapunov Systems

2009 ◽  
Vol 19 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Przemysław Przyborowski ◽  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Positive 2D Discrete-Time Linear Lyapunov SystemsTwo models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

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