scholarly journals Exponential Synchronization for Impulsive Dynamical Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Lijun Pan ◽  
Jinde Cao
Keyword(s):  
Differential Inequality ◽  
Discrete System ◽  
Kronecker Product ◽  
Exponential Synchronization ◽  
Impulsive Effects ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Linear Discrete System ◽  
Theoretical Results ◽  
Impulsive Differential Inequality

This paper is devoted to exponential synchronization for complex dynamical networks with delay and impulsive effects. The coupling configuration matrix is assumed to be irreducible. By using impulsive differential inequality and the Kronecker product techniques, some criteria are obtained to guarantee the exponential synchronization for dynamical networks. We also extend the delay fractioning approach to the dynamical networks by constructing a Lyapunov-Krasovskii functional and comparing to a linear discrete system. Meanwhile, numerical examples are given to demonstrate the theoretical results.

scholarly journals Effects of Time-Varying Impulses on the Synchronization of Delayed Dynamical Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shuiming Cai ◽  
Peipei Zhou ◽  
Zengrong Liu
Keyword(s):  
Network Model ◽  
Comparison Principle ◽  
Network Topology ◽  
Spanning Tree ◽  
Time Varying ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
General Complex ◽  
Delayed Dynamical Networks ◽  
Theoretical Results

The effects of time-varying impulses on the synchronization of a class of general complex delayed dynamical networks are investigated. Different from the existing works, the impulses discussed here are time-varying, and both synchronizing and desynchronizing impulses are considered in the network model simultaneously. Moreover, the network topology is assumed to be directed and weakly connected with a spanning tree. By using the comparison principle, some simple yet generic globally exponential synchronization criteria are derived. It is shown that besides impulse strengths and impulsive interval, the obtained criteria are also closely related with topology structure of the network. Finally, numerical examples are given to demonstrate the effectiveness of the theoretical results.

scholarly journals Pinning Adaptive Synchronization of Delayed Coupled Dynamical Networks via Periodically Intermittent Control

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Xueliang Liu ◽  
Shengbing Xu
Keyword(s):  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Adaptive Synchronization ◽  
Intermittent Control ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Periodically Intermittent Control ◽  
Synchronization Problem ◽  
Theoretical Results

This paper investigates the exponential synchronization problem of delayed coupled dynamical networks by using adaptive pinning periodically intermittent control. Based on the Lyapunov method, by designing adaptive feedback controller, some sufficient conditions are presented to ensure the exponential synchronization of coupled dynamical networks with delayed coupling. Furthermore, a numerical example is given to demonstrate the validity of the theoretical results.

Finite-time outer synchronization between two complex dynamical networks with on–off coupling

2015 ◽  
Vol 26 (08) ◽  
pp. 1550095 ◽  
Author(s):  
Yan Dong ◽  
Junwei Chen
Keyword(s):  
Lyapunov Function ◽  
Coupling Strength ◽  
Finite Time ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Outer Synchronization ◽  
Time Differential ◽  
Theoretical Results

In this paper, the finite-time outer synchronization between two complex dynamical networks with on–off coupling is investigated. By using suitable on–off controllers, sufficient conditions for finite-time outer synchronization are derived based on the Lyapunov function and the finite-time differential inequality method. The theoretical results imply that the two networks will achieve finite-time outer synchronization for fixed on–off rate if the control coupling strength is large enough. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 693-704 ◽  
Author(s):  
Kaifang Fei ◽  
Minghui Jiang ◽  
Meng Yan ◽  
Weizhen Liu
Keyword(s):  
Neural Networks ◽  
State Feedback ◽  
Exponential Synchronization ◽  
Matrix Measure ◽  
Analysis Techniques ◽  
Discontinuous Activations ◽  
Inclusion Theory ◽  
Generalized Halanay Inequality ◽  
New Criteria ◽  
Theoretical Results

AbstractIn this paper, the matters of dissipativity and synchronization for non-autonomous Hopfield neural networks with discontinuous activations are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. The global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, the global exponential synchronization of the addressed network drive system and the response system is realized by utilizing inequality and some analysis techniques and designing the discontinuous state feedback controller. Finally, several numerical examples are given to verify the validity of the theoretical results.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

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