Halanay inequality involving Caputo-Hadamard fractional derivative and application

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed D. Kassim ◽  
Nasser-eddine Tatar
Keyword(s):  
Distributed Delay ◽  
Hopfield Neural Network ◽  
Network System ◽  
Logarithmic Function ◽  
Halanay Inequality ◽  
General Sufficient Condition ◽  
Decay Of Solutions ◽  
Neural Network System ◽  
Fractional Differential ◽  
Hadamard Derivative

Abstract A Halanay inequality with distributed delay of non-convolution type is considered. We establish a decay of solutions as a Mittag-Leffler function composed with a logarithmic function. A general sufficient condition is found and a large class of admissible retardation kernels is provided. This needs the preparation of several lemmas on properties of the Hadamard derivative and some basic fractional differential problems with this kind of derivative. The obtained result is then applied to a Hopfield neural network system to discuss its stability.

OLFACTORY NEURAL NETWORK MODEL

1992 ◽  
Vol 06 (27) ◽  
pp. 1721-1728
Author(s):  
N. KAZAKOVA ◽  
VIK. DOTSENKO
Keyword(s):  
Neural Network ◽  
Phase Diagram ◽  
Mean Field ◽  
Hopfield Neural Network ◽  
Network System ◽  
Zero Temperature ◽  
Field Phase ◽  
Simple Generalization ◽  
Neural Network System ◽  
Olfactory Neural Network

A statistical neural network olfactory model is proposed. The model is a simple generalization of the Hopfield neural network system. Retrieval properties are analysed and the zero temperature mean field phase diagram is obtained.

scholarly journals A neutral fractional Halanay inequality and application to a Cohen-Grossberg neural network system

2021 ◽  
Author(s):  
Mohammed Kassim ◽  
Nasser-eddine Tatar
Keyword(s):  
Neural Network ◽  
Fractional Derivative ◽  
Neutral Type ◽  
Network System ◽  
Network Systems ◽  
Large Classes ◽  
Halanay Inequality ◽  
Order Case ◽  
Neural Network System ◽  
Fractional Halanay Inequality

We extend the well-known Halanay inequality to the fractional order case in presence of distributed delays and delays of neutral type (in the fractional derivative). Both the discrete and distributed neutral delays are investigated. It is proved that solutions decay toward zero in a Mittag-Leffler manner under some rather general conditions. Some large classes of kernels and examples satisfying our assumptions are provided. We apply our findings to prove Mittag-Leffler stability for solutions of fractional neutral network systems of Cohen-Grossberg type.

scholarly journals Arbitrary stability for a Hopfield neural network problem with discrete and distributed delays

2021 ◽  
Author(s):  
Mohammed Kassim ◽  
Nasser-eddine Tatar
Keyword(s):  
Neural Network ◽  
Stability Result ◽  
Hopfield Neural Network ◽  
Distributed Delays ◽  
Network System ◽  
Power Type ◽  
Arbitrary Type ◽  
Special Cases ◽  
Neural Network System ◽  
Judicious Choice

We consider a Hopfield neural network system containing discrete as well as distributed delays. A stability result of arbitrary type is proved under weaker assumptions than the used ones so far. This result includes exponential and polynomial (or power type) stability as special cases. Our proof relies on a judicious choice of Lyapunov-type functionals and some appropriate manipulations.

scholarly journals Novel artificial intelligent/neural network system for staging of nonalcoholic steatohepatitis

2021 ◽  
Author(s):  
Takeshi Okanoue ◽  
Toshihide Shima ◽  
Yasuhide Mitsumoto ◽  
Atsushi Umemura ◽  
Kanji Yamaguchi ◽  
...  
Keyword(s):  
Neural Network ◽  
Nonalcoholic Steatohepatitis ◽  
Network System ◽  
Artificial Intelligent ◽  
Neural Network System
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