scholarly journals Synchronization Analysis for Stochastic Inertial Memristor-Based Neural Networks with Linear Coupling

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Lixia Ye ◽  
Yonghui Xia ◽  
Jin-liang Yan ◽  
Haidong Liu
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Parametric Uncertainty ◽  
Uncertain System ◽  
Linear Coupling ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Varying Delay ◽  
Theoretical Results

This paper concerns the synchronization problem for a class of stochastic memristive neural networks with inertial term, linear coupling, and time-varying delay. Based on the interval parametric uncertainty theory, the stochastic inertial memristor-based neural networks (IMNNs for short) with linear coupling are transformed to a stochastic interval parametric uncertain system. Furthermore, by applying the Lyapunov stability theorem, the stochastic analysis approach, and the Halanay inequality, some sufficient conditions are obtained to realize synchronization in mean square. The established criteria show that stochastic perturbation is designed to ensure that the coupled IMNNs can be synchronized better by changing the state coefficients of stochastic perturbation. Finally, an illustrative example is presented to demonstrate the efficiency of the theoretical results.

scholarly journals Projective synchronization analysis for BAM neural networks with time-varying delay via novel control

2021 ◽  
Vol 26 (1) ◽  
pp. 41-56
Author(s):  
Malika Sader ◽  
Fuyong Wang ◽  
Zhongxin Liu ◽  
Zhongxin Chen
Keyword(s):  
Neural Networks ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Application Process ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Varying Delay ◽  
Theoretical Results

In this paper, the projective synchronization of BAM neural networks with time-varying delays is studied. Firstly, a type of novel adaptive controller is introduced for the considered neural networks, which can achieve projective synchronization. Then, based on the adaptive controller, some novel and useful conditions are obtained to ensure the projective synchronization of considered neural networks. To our knowledge, different from other forms of synchronization, projective synchronization is more suitable to clearly represent the nonlinear systems’ fragile nature. Besides, we solve the projective synchronization problem between two different chaotic BAM neural networks, while most of the existing works only concerned with the projective synchronization chaotic systems with the same topologies. Compared with the controllers in previous papers, the designed controllers in this paper do not require any activation functions during the application process. Finally, an example is provided to show the effectiveness of the theoretical results.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Global Robust Exponential Dissipativity for Interval Recurrent Neural Networks with Infinity Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohong Wang ◽  
Huan Qi
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Activation Functions ◽  
Time Varying Delay ◽  
Distributed Time Delay ◽  
General Activation ◽  
Attractive Sets ◽  
Varying Delay

This paper is concerned with the robust dissipativity problem for interval recurrent neural networks (IRNNs) with general activation functions, and continuous time-varying delay, and infinity distributed time delay. By employing a new differential inequality, constructing two different kinds of Lyapunov functions, and abandoning the limitation on activation functions being bounded, monotonous and differentiable, several sufficient conditions are established to guarantee the global robust exponential dissipativity for the addressed IRNNs in terms of linear matrix inequalities (LMIs) which can be easily checked by LMI Control Toolbox in MATLAB. Furthermore, the specific estimation of positive invariant and global exponential attractive sets of the addressed system is also derived. Compared with the previous literatures, the results obtained in this paper are shown to improve and extend the earlier global dissipativity conclusions. Finally, two numerical examples are provided to demonstrate the potential effectiveness of the proposed results.

ROBUST SYNCHRONIZATION CRITERIA FOR RECURRENT NEURAL NETWORKS VIA LINEAR FEEDBACK

2007 ◽  
Vol 17 (08) ◽  
pp. 2723-2738 ◽  
Author(s):  
XIA HUANG ◽  
JAMES LAM ◽  
JINDE CAO ◽  
SHENGYUAN XU
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Feedback ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Control Robustness ◽  
Delay Dependent

In this paper, the robust synchronization problem is addressed for recurrent neural networks with time-varying delay by linear feedback control. Robustness in the present paper is referred to as the allowance of parameters mismatch between the drive system and the response system. Sufficient conditions for robust synchronization with a synchronization error bound, expressed as linear matrix inequality (LMI), are derived based on Lyapunov–Krasovskii functionals. Both delay-dependent and delay-independent conditions are obtained. Two examples are given to illustrate the results.

Fixed-time synchronization of quaternion-valued neural networks with time-varying delay

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200324
Author(s):  
Umesh Kumar ◽  
Subir Das ◽  
Chuangxia Huang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Fixed Time ◽  
Time Varying ◽  
Activation Functions ◽  
Time Varying Delay ◽  
The Neural Networks ◽  
Varying Delay

In this article, sufficient conditions for fixed-time synchronization of time-delayed quaternion-valued neural networks (QVNNs) are derived. Firstly, QVNNs are decomposed into four real-valued systems. Then using the available lemmas and by constructing the Lyapunov function, the synchronization criterion for the neural networks is proposed. Activation functions satisfy the Lipschitz condition. A suitable controller has been designed to synchronize the master–slave systems. The effectiveness of the proposed result is validated through a comparison of the settling time obtained by applying two different existing lemmas to a particular problem of synchronization of two identical QVNNs with time-varying delay with the help of suitable controllers.

scholarly journals Synchronization of Caputo fractional neural networks with bounded time variable delays

2021 ◽  
Vol 19 (1) ◽  
pp. 388-399
Author(s):  
Ricardo Almeida ◽  
Snezhana Hristova ◽  
Stepan Tersian
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Variable ◽  
Rate Of Change ◽  
Time Varying ◽  
Time Varying Delay ◽  
Variable Delays ◽  
Varying Delay

Abstract One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the j j th neuron to the i i th neuron) are variable in time and unbounded. The rate of change of the dynamics of all neurons is described by the Caputo fractional derivative. We apply Lyapunov functions and the Razumikhin method to obtain some sufficient conditions to ensure synchronization in the model. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. We illustrate our theory with a particular nonlinear neural network.

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 Robust Finite-time Boundedness of Discrete-time Neural Networks with Time-varying Delays

2021 ◽  
Vol 17 ◽  
pp. 146-155
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

This paper is concerned with the problem of robust finite-time boundedness for the discrete-time neural networks with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii functional, we propose the sufficient conditions which ensure the robust finite-time boundedness of the discrete-time neural networks with time-varying delay in terms of linear matrix inequalities. Then the sufficient conditions of robust finite-time stability for the discrete-time neural networks with time-varying delays are given. Finally, a numerical example is presented to illustrate the efficiency of proposed methods.

Stability analysis and stabilization of a class of discrete-time nonlinear switched systems with time-delay and affine parametric uncertainty

2019 ◽  
Vol 25 (7) ◽  
pp. 1326-1340 ◽  
Author(s):  
N.A. Baleghi ◽  
M.H. Shafiei
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Parametric Uncertainty ◽  
Switched System ◽  
Time Varying Delay ◽  
Nonlinear Switched Systems ◽  
The Stability ◽  
Varying Delay ◽  
Special Case

This paper presents stability analysis and stabilization of a nonlinear switched system with subsystems which involve time-varying delay, nonlinear terms, and affine parametric uncertainties. The main goal of this paper is to construct a state-feedback controller to stabilize the closed-loop switched system, and as a special case to derive sufficient conditions to guarantee the stability of the uncontrolled switched system. In this regard, based on switched Lyapunov functions, an appropriate Lyapunov–Krasovskii functional is constructed to establish the sufficient conditions; these conditions depend only on the upper bounds of the time-delay, uncertain parameters, and the maximal bound of the nonlinear term. Finally, numerical examples are provided to verify the theoretical results and to compare the obtained results with previous researches.

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