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>

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.

scholarly journals On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 335 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Stanislav Simeonov ◽  
Ivan Torlakov
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Stability Criteria ◽  
Bidirectional Associative Memory ◽  
The Neural Network ◽  
Lyapunov Function Method ◽  
Impulsive Perturbations ◽  
The Stability

The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

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