scholarly journals Robust Stability Analysis of Fractional-Order Hopfield Neural Networks with Parameter Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Shuo Zhang ◽  
Yongguang Yu ◽  
Wei Hu
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Robust Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Neural System ◽  
Hopfield Neural Networks ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Theoretical Results

The issue of robust stability for fractional-order Hopfield neural networks with parameter uncertainties is investigated in this paper. For such neural system, its existence, uniqueness, and global Mittag-Leffler stability of the equilibrium point are analyzed by employing suitable Lyapunov functionals. Based on the fractional-order Lyapunov direct method, the sufficient conditions are proposed for the robust stability of the studied networks. Moreover, robust synchronization and quasi-synchronization between the class of neural networks are discussed. Furthermore, some numerical examples are given to show the effectiveness of our obtained theoretical results.

Robust stability analysis for delayed Cohen-Grossberg-type bidirectional associative memory neural networks with norm-bounded uncertainties

2009 ◽  
Vol 223 (5) ◽  
pp. 693-707
Author(s):  
Y Wang ◽  
P Hu
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Bidirectional Associative Memory ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Global Robust Stability ◽  
Bounded Uncertainties

In this paper, the problem of global robust stability is discussed for uncertain Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with delays. The parameter uncertainties are supposed to be norm bounded. The sufficient conditions for global robust stability are derived by employing a Lyapunov-Krasovskii functional. Based on these, the conditions ensuring global asymptotic stability without parameter uncertainties are established. All conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, two examples are provided to illustrate the effectiveness of the results obtained.

scholarly journals Stability and Hopf-Bifurcating Periodic Solution for Delayed Hopfield Neural Networks withnNeuron

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Haji Mohammad Mohammadinejad ◽  
Mohammad Hadi Moslehi
Keyword(s):  
Neural Networks ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Neural System ◽  
Hopfield Neural Networks ◽  
Local Asymptotic Stability ◽  
Trivial Equilibrium ◽  
Delay Differential ◽  
Bifurcating Periodic Solution ◽  
Theoretical Results

We consider a system of delay differential equations which represents the general model of a Hopfield neural networks type. We construct some new sufficient conditions for local asymptotic stability about the trivial equilibrium based on the connection weights and delays of the neural system. We also investigate the occurrence of an Andronov-Hopf bifurcation about the trivial equilibrium. Finally, the simulating results demonstrate the validity and feasibility of our theoretical results.

Global robust stability of complex-valued recurrent neural networks with time-delays and uncertainties

2014 ◽  
Vol 07 (02) ◽  
pp. 1450016 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Recurrent Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Neural System ◽  
Multiple Time ◽  
Parameter Uncertainties ◽  
Global Robust Stability ◽  
Complex Valued

This paper focuses on the existence, uniqueness and global robust stability of equilibrium point for complex-valued recurrent neural networks with multiple time-delays and under parameter uncertainties with respect to two activation functions. Two sufficient conditions for robust stability of the considered neural networks are presented and established in two new time-independent relationships between the network parameters of the neural system. Finally, three illustrative examples are given to demonstrate the theoretical results.

scholarly journals Robust stability analysis of impulsive quaternion-valued neural networks with distributed delays and parameter uncertainties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jielin Zhou ◽  
Yuanshun Tan ◽  
Xiaofeng Chen ◽  
Zijian Liu
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Mapping Method ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Lyapunov Stability Theorem ◽  
Parameter Uncertainties ◽  
Lmi Approach ◽  
Robust Stability Analysis

AbstractIn this paper, an impulsive quaternion-valued neural networks (QVNNs) model with leakage, discrete, and distributed delays is considered. Based on the homeomorphic mapping method, Lyapunov stability theorem, and linear matrix inequality (LMI) approach, sufficient conditions for the existence, uniqueness, and global robust stability of the equilibrium point of the impulsive QVNNs are provided. A numerical example is provided to confirm the obtained results. A conclusion is presented in the end.

scholarly journals New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Weiwei Zhang ◽  
Jinde Cao ◽  
Ahmed Alsaedi ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
Delayed Neural Networks ◽  
New Methods ◽  
Theoretical Results

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order α, 0<α≤1/2 and 1/2<α<1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finite-time interval. Numerical example is given to verify the feasibility of the theoretical results.

Global stabilization of memristor-based fractional-order neural networks with delay via output-feedback control

2017 ◽  
Vol 31 (05) ◽  
pp. 1750031 ◽  
Author(s):  
Jiyang Chen ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Xujun Yang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Output Feedback ◽  
Differential Inclusions ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Global Stabilization ◽  
Lyapunov Direct Method ◽  
Stabilizing Control

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.

Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties

2021 ◽  
Vol 420 ◽  
pp. 70-81
Author(s):  
Qiankun Song ◽  
Yanxi Chen ◽  
Zhenjiang Zhao ◽  
Yurong Liu ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Robust Stability ◽  
Parameter Uncertainties
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