Global asymptotic stability of a larger class of neural networks with constant time delay

2003 ◽  
Vol 311 (6) ◽  
pp. 504-511 ◽  
Author(s):  
Sabri Arik
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Constant Time Delay ◽  
Constant Time

scholarly journals Global Stability Analysis of Neural Networks with Constant Time Delay via Frobenius Norm

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
N. Mohamed Thoiyab ◽  
P. Muruganantham ◽  
Grienggrai Rajchakit ◽  
Nallappan Gunasekaran ◽  
Bundit Unyong ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Lyapunov Functional ◽  
Constant Time Delay ◽  
Constant Time ◽  
Frobenius Norm ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Global Stability Analysis ◽  
Bounded Functions

This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters.

Stability for Hopfield Neural Networks With Time Delay

2002 ◽  
Vol 8 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Linshan Wang ◽  
Daoyi Xu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Hopfield Neural Networks ◽  
Unique Equilibrium ◽  
Transmission Delays

In this paper, the global asymptotic stability of the equilibrium point of Hopfield neural networks with interneuronal transmission delays is studied. Some sufficient conditions related to the existence of a unique equilibrium point and its global asymptotic stability are derived.

Global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay

2017 ◽  
Vol 243 ◽  
pp. 49-59 ◽  
Author(s):  
Limin Wang ◽  
Qiankun Song ◽  
Yurong Liu ◽  
Zhenjiang Zhao ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Fractional Order ◽  
Global Asymptotic Stability ◽  
Order Complex ◽  
Complex Valued

NOVEL STABILITY CONDITIONS FOR CELLULAR NEURAL NETWORKS WITH TIME DELAY

2001 ◽  
Vol 11 (07) ◽  
pp. 1853-1864 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
JUEBANG YU
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Research Work ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Time Varying Delay

In this paper, the global asymptotic stability of cellular neural networks with time delay is discussed using some novel Lyapunov functionals. Novel sufficient conditions for this type of stability are derived. They are less restrictive and more practical than those currently used. As a result, the design of cellular neural networks with time delay is refined. Our work can also be generalized to cellular neural networks with time-varying delay, a topic on which little research work has been done. By means of several different Lyapunov functionals, some sufficient conditions related to the global asymptotic stability for cellular neural networks with perturbations of time-varying delays are derived.

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