scholarly journals On the stability with respect to manifolds of reaction-diffusion impulsive control fractional-order neural networks with time-varying delays

2021 ◽  
Author(s):  
Gani Stamov ◽  
Trayan Stamov ◽  
Ivanka Stamova
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Impulsive Control ◽  
Reaction Diffusion ◽  
Time Varying ◽  
The Stability

scholarly journals Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jinhua Huang ◽  
Jiqing Liu ◽  
Guopeng Zhou
Keyword(s):  
Neural Networks ◽  
Boundary Condition ◽  
Diffusion Coefficients ◽  
Global Exponential Stability ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Dirichlet Laplacian ◽  
The Stability

This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.

scholarly journals Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 138
Author(s):  
Zhixin Zhang ◽  
Yufeng Zhang ◽  
Jia-Bao Liu ◽  
Jiang Wei
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Asymptotical Stability ◽  
Time Varying ◽  
Global Asymptotical Stability ◽  
Stability Criteria ◽  
Lmi Approach ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

In this paper, the global asymptotical stability of Riemann-Liouville fractional-order neural networks with time-varying delays is studied. By combining the Lyapunov functional function and LMI approach, some sufficient criteria that guarantee the global asymptotical stability of such fractional-order neural networks with both discrete time-varying delay and distributed time-varying delay are derived. The stability criteria is suitable for application and easy to be verified by software. Lastly, some numerical examples are presented to check the validity of the obtained results.

Delayed Reaction–Diffusion Cellular Neural Networks of Fractional Order: Mittag–Leffler Stability and Synchronization

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Ivanka M. Stamova ◽  
Stanislav Simeonov
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Delayed Reaction

This research introduces a model of a delayed reaction–diffusion fractional neural network with time-varying delays. The Mittag–Leffler-type stability of the solutions is investigated, and new sufficient conditions are established by the use of the fractional Lyapunov method. Mittag–Leffler-type synchronization criteria are also derived. Three illustrative examples are established to exhibit the proposed sufficient conditions.

MEAN VALUE EXPONENTIAL STABILITY OF STOCHASTIC REACTION–DIFFUSION GENERALIZED COHEN–GROSSBERG NEURAL NETWORKS WITH TIME-VARYING DELAY

2007 ◽  
Vol 17 (09) ◽  
pp. 3219-3227 ◽  
Author(s):  
LI WAN ◽  
QINGHUA ZHOU ◽  
JIANHUA SUN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Mean Value ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Stochastic Reaction ◽  
Varying Delay

Stochastic effects on the stability property of reaction–diffusion generalized Cohen–Grossberg neural networks (GDCGNNs) with time-varying delay are considered. By skillfully constructing suitable Lyapunov functionals and employing the method of variational parameters, inequality technique and stochastic analysis, the delay independent and easily verifiable sufficient conditions to guarantee the mean-value exponential stability of an equilibrium solution associated with temporally uniform external inputs to the networks are obtained. One example is given to illustrate the theoretical results.

scholarly journals Synchronization of Fractional Order Fuzzy BAM Neural Networks With Time Varying Delays and Reaction Diffusion Terms

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 186551-186571
Author(s):  
M. Syed Ali ◽  
M. Hymavathi ◽  
Grienggrai Rajchakit ◽  
Sumit Saroha ◽  
L. Palanisamy ◽  
...  
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Fuzzy Bam Neural Networks

Mittag-Leffler stability of impulsive fractional-order bi-directional associative memory neural networks with time-varying delays

2017 ◽  
Vol 40 (10) ◽  
pp. 3068-3077 ◽  
Author(s):  
Ivanka Stamova ◽  
Gani Stamov ◽  
Stanislav Simeonov ◽  
Alexander Ivanov
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Associative Memory ◽  
Lyapunov Method ◽  
Impulsive Control ◽  
Control Law ◽  
Sufficient Condition ◽  
Time Varying ◽  
Delay Model ◽  
Network Time

In the paper, a class of impulsive Caputo fractional-order bi-directional associative memory neural networks with time-varying delays is considered. Applying the fractional Lyapunov method, a sufficient condition for Mittag-Leffler stability of the equilibrium point of the system under consideration is derived. Some earlier results are extended and improved. Our results provide an impulsive control law which stabilizes the impulse-free fractional-order neural network time-delay model. An example is provided to demonstrate the effectiveness of the proposed results.

scholarly journals $ S $-asymptotically $ \omega $-periodic dynamics in a fractional-order dual inertial neural networks with time-varying lags

2021 ◽  
Vol 7 (2) ◽  
pp. 2782-2809
Author(s):  
Huizhen Qu ◽  
◽  
Jianwen Zhou
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Periodic Oscillation ◽  
Global Dynamics ◽  
Time Lags ◽  
Time Varying ◽  
Stability Criteria ◽  
Inertial Neural Networks ◽  
Periodic Dynamics ◽  
The Stability

<abstract><p>This paper investigates global dynamics in fractional-order dual inertial neural networks with time lags. Firstly, according to some crucial features of Mittag-Leffler functions and Banach contracting mapping principle, the existence and uniqueness of $ S $-asymptotically $ \omega $-periodic oscillation of the model are gained. Secondly, by using the comparison principle and the stability criteria of delayed Caputo fractional-order differential equations, global asymptotical stability of the model is studied. In the end, the feasibility and effectiveness of the obtained conclusions are supported by two numerical examples. There are few papers focus on $ S $-asymptotically $ \omega $-periodic dynamics in fractional-order dual inertial neural networks with time-varying lags, apparently, the works in this paper fill some of the gaps.</p></abstract>

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