SYNCHRONIZATION IN LINEARLY COUPLED DYNAMICAL NETWORKS WITH DISTRIBUTED TIME DELAYS

2008 ◽  
Vol 18 (07) ◽  
pp. 2039-2047 ◽  
Author(s):  
CHUN-HSIEN LI ◽  
SUH-YUH YANG
Keyword(s):  
Lyapunov Functional ◽  
Time Delays ◽  
Exponential Synchronization ◽  
Matrix Inequality ◽  
Dynamical Networks ◽  
Distributed Time Delays ◽  
Inequality Techniques ◽  
Simulation Results ◽  
Global Exponential Synchronization ◽  
Theoretical Analyses

In this paper, we investigate the global exponential synchronization of linearly coupled dynamical networks with time delays. The time delay considered is of the distributed type and the outer-coupling matrix is not assumed to be symmetric. Employing the Lyapunov functional and matrix inequality techniques, we propose a sufficient condition for the occurrence of global exponential synchronization. Two illustrative examples, the coupled Chua's circuits and the coupled Hindmarsh–Rose neurons, and their numerical simulation results are presented to demonstrate the theoretical analyses.

scholarly journals Exponential Synchronization in Inertial Neural Networks with Time Delays

Electronics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 356 ◽  
Author(s):  
Liang Ke ◽  
Wanli Li
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Lyapunov Functional ◽  
Time Delays ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Inertial Neural Networks ◽  
Response Systems ◽  
Global Exponential Synchronization

In this paper, exponential synchronization for inertial neural networks with time delays is investigated. First, by introducing a directive Lyapunov functional, a sufficient condition is derived to ascertain the global exponential synchronization of the drive and response systems based on feedback control. Second, by introducing a variable substitution, the second-order differential equation is transformed into a first-order differential equation. As such, a new Lyapunov functional is constructed to formulate a novel global exponential synchronization for the systems under study. The two obtained sufficient conditions complement each other and are suitable to be applied in different cases. Finally, two numerical examples are given to illustrated the effectiveness of the proposed theoretical results.

scholarly journals Global exponential synchronization of quaternion-valued memristive neural networks with time delays

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Ruoyu Wei ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Differential Inclusion ◽  
Lyapunov Functional ◽  
Time Delays ◽  
Exponential Synchronization ◽  
The Other ◽  
Memristive Neural Networks ◽  
Global Synchronization ◽  
New Class ◽  
Inequality Techniques

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper.

Robust Output Observer-Based Control of Neutral Uncertain Systems with Discrete and Distributed Time Delays

2015 ◽  
Vol 764-765 ◽  
pp. 629-633
Author(s):  
Jenq Der Chen ◽  
I Te Wu ◽  
Chin Tan Lee ◽  
Ruey Shin Chen ◽  
Chyi Da Yang
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Matrix Inequality ◽  
Neutral Systems ◽  
Lmi Optimization ◽  
Distributed Time Delays ◽  
Matrix Equality ◽  
Dynamic Observer

In this paper, the robust control problem of output dynamic observer-based control for a class of uncertain neutral systems with discrete and distributed time delays is considered. Linear matrix inequality (LMI) optimization approach is used to design the new output dynamic observer-based controls. Three classes of observer-based controls are proposed and the maximal perturbed bound is given. Based on the results of this paper, the constraint of matrix equality is not necessary for designing the observer-based controls.

Synchronization stability on the BAM neural networks with mixed time delays

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Bidirectional Associative Memory ◽  
Mixed Time Delays ◽  
Distributed Time Delays ◽  
Inequality Techniques

AbstractThis article investigates the general decay synchronization (GDS) for the bidirectional associative memory neural networks (BAMNNs). Compared with previous research results, both time-varying delays and distributed time delays are taken into consideration. By using Lyapunov method and using useful inequality techniques, some sufficient conditions on the GDS for BAMNNs are derived. Finally, a numerical example is also carried out to validate the practicability and feasibility of our proposed results. It is worth pointing out that the GDS may be specialized as exponential synchronization, polynomial synchronization and logarithmic synchronization. Besides, we can estimate the convergence rate of the synchronization by GDS. The obtained results in this article can be seen as the improvement and extension of the previously known works.

scholarly journals Global Robust Exponential Synchronization of Multiple Uncertain Neural Networks Subject to Event-Triggered Strategy

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Jin-E Zhang ◽  
Huan Liu
Keyword(s):  
Neural Networks ◽  
Parameter Uncertainty ◽  
Sampling Time ◽  
Exponential Synchronization ◽  
Matrix Inequality ◽  
Time Intervals ◽  
Laplace Matrix ◽  
Multiple Neural Networks ◽  
Inequality Techniques ◽  
Event Triggered

This paper proposes the event-triggered strategy (ETS) for multiple neural networks (NNs) with parameter uncertainty and time delay. By establishing event-triggered mechanism and using matrix inequality techniques, several sufficient criteria are obtained to ensure global robust exponential synchronization of coupling NNs. In particular, the coupling matrix need not be the Laplace matrix in this paper. In addition, the lower bounds of sampling time intervals are also found by the established event-triggered mechanism. Eventually, three numerical examples are offered to illustrate the obtained results.

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