scholarly journals Synchronization of Intermittently Coupled Dynamical Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Gang Zhang ◽  
Guanrong Chen
Keyword(s):  
Coupling Strength ◽  
Stability Theory ◽  
Lorenz System ◽  
Impulsive Differential Equations ◽  
Time Varying ◽  
Coupling Matrix ◽  
Dynamical Networks ◽  
Dynamical Network ◽  
The Stability ◽  
Theoretical Results

This paper investigates the synchronization phenomenon of an intermittently coupled dynamical network in which the coupling among nodes can occur only at discrete instants and the coupling configuration of the network is time varying. A model of intermittently coupled dynamical network consisting of identical nodes is introduced. Based on the stability theory for impulsive differential equations, some synchronization criteria for intermittently coupled dynamical networks are derived. The network synchronizability is shown to be related to the second largest and the smallest eigenvalues of the coupling matrix, the coupling strength, and the impulsive intervals. Using the chaotic Chua system and Lorenz system as nodes of a dynamical network for simulation, respectively, the theoretical results are verified and illustrated.

Synchronization in Drive-Response Dynamical Networks Based on Nonlinear Control

2013 ◽  
Vol 791-793 ◽  
pp. 652-657
Author(s):  
Dong Dong Feng
Keyword(s):  
Coupling Strength ◽  
Stability Theory ◽  
Lorenz System ◽  
Sufficient Conditions ◽  
Small World ◽  
Nonlinear Controller ◽  
Dynamical Networks ◽  
Scale Free ◽  
Simulation Results ◽  
The Stability

In this paper, synchronization in drive-response dynamical networks is investigated. By using the Gerschgorins disk theorem and the stability theory, a nonlinear controller is designed to make the drive-response dynamical networks synchronized. Some sufficient conditions for achieving the synchronization of the drive-response dynamical networks are derived. The structure of the network can be random, regular, small-world, or scale-free. A numerical example is given to demonstrate the validity of the proposed method, in which the famous Lorenz system is chosen as the nodes of the network. Simulation results have verified the correctness and effectiveness of the proposed scheme. Moreover, it is worth noting that the time used for achieving synchronization of the drive-response dynamical networks sensitively depends on the coupling strength .

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.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

Reduced-order observer-based consensus control of linear multi-agent systems over directed networks with nonuniform communication delays

2020 ◽  
pp. 014233122093430
Author(s):  
Qiuzhen Wang ◽  
Jiangping Hu ◽  
Yiyi Zhao ◽  
Bijoy Kumar Ghosh
Keyword(s):  
Time Varying ◽  
Communication Delays ◽  
Multi Agent Systems ◽  
Consensus Control ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Multi Agent ◽  
The Stability ◽  
Output Information ◽  
Theoretical Results

This paper considers a consensus control of a general linear multi-agent system with time-varying communication delays. Since each agent can only use the relative output information from its neighbors, a reduced-order observer-based control protocol is proposed to guarantee consensus on the directed communication network. The stability of the closed-loop system is analyzed for the cases with uniform delays and nonuniform time-varying delays, respectively. Moreover, the upper bounds of the communication delays are obtained respectively for the two cases. Finally, two numerical examples are provided to illustrate the proposed theoretical results.

scholarly journals Adaptive Aperiodically Intermittent Synchronization for Complex Dynamical Network with Unknown Time-Varying Outer Coupling Strengths

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Lihong Yan ◽  
Junmin Li
Keyword(s):  
Adaptive Learning ◽  
Exponential Synchronization ◽  
Intermittent Control ◽  
Time Varying ◽  
Complex Dynamical Network ◽  
Dynamical Network ◽  
Synchronization Problem ◽  
Coupling Strengths ◽  
Inequality Techniques ◽  
Theoretical Results

In this paper, exponential synchronization problem of complex dynamical networks with unknown periodically coupling strengths was investigated. An aperiodically intermittent control synchronization strategy is proposed. Based on Lyapunov exponential stability theory, inequality techniques, and adaptive learning laws design, some sufficient exponential synchronization criteria for complex dynamical network with unknown periodical coupling weights are obtained. The numerical simulation example is presented to illustrate the feasibility of theoretical results.

Partial stability analysis of nonlinear time-varying impulsive systems

2019 ◽  
Vol 12 (06) ◽  
pp. 1950066
Author(s):  
Boulbaba Ghanmi
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Time Varying ◽  
Impulsive Systems ◽  
Partial Stability ◽  
Stability Theorems ◽  
Time Varying Systems ◽  
The Stability ◽  
Derivatives Of ◽  
Theoretical Results

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

SYNCHRONIZATION IN SMALL-WORLD DYNAMICAL NETWORKS

2002 ◽  
Vol 12 (01) ◽  
pp. 187-192 ◽  
Author(s):  
XIAO FAN WANG ◽  
GUANRONG CHEN
Keyword(s):  
Dynamical Systems ◽  
Coupling Strength ◽  
Continuous Time ◽  
Nearest Neighbor ◽  
Small World ◽  
Small World Network ◽  
Dynamical Networks ◽  
Dynamical Network ◽  
Number Of Cells

We investigate synchronization in a network of continuous-time dynamical systems with small-world connections. The small-world network is obtained by randomly adding a small fraction of connection in an originally nearest-neighbor coupled network. We show that, for any given coupling strength and a sufficiently large number of cells, the small-world dynamical network will synchronize, even if the original nearest-neighbor coupled network cannot achieve synchronization under the same condition.

scholarly journals Projective Synchronization Analysis of Drive-Response Coupled Dynamical Network with Multiple Time-Varying Delays via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Multiple Time ◽  
Time Varying ◽  
Comparison Theory ◽  
Dynamical Network ◽  
Functional Differential ◽  
The Stability ◽  
System Nodes

The problem of projective synchronization of drive-response coupled dynamical network with delayed system nodes and multiple coupling time-varying delays is investigated. Some sufficient conditions are derived to ensure projective synchronization of drive-response coupled network under the impulsive controller by utilizing the stability analysis of the impulsive functional differential equation and comparison theory. Numerical simulations on coupled time delay Lorenz chaotic systems are exploited finally to illustrate the effectiveness of the obtained results.

scholarly journals Adaptive-Impulsive Control of the Projective Synchronization in Drive-Response Complex Dynamical Networks with Time-Varying Coupling

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Song Zheng
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Projective Synchronization ◽  
Time Varying ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Hybrid Controller ◽  
The Stability ◽  
Response Complex

This paper investigates the projective synchronization (PS) of drive-response time-varying coupling complex dynamical networks with time delay via an adaptive-impulsive controlling method, in which the weights of links are time varying. Based on the stability analysis of impulsive control system, sufficient conditions for the PS are derived, and a hybrid controller, that is, an adaptive feedback controller with impulsive control effects, is designed. Numerical simulations are performed to verify the correctness and effectiveness of theoretical result.

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