Synchronization in scale-free dynamical networks: robustness and fragility

2002 ◽  
Vol 49 (1) ◽  
pp. 54-62 ◽  
Author(s):  
Xiao Fan Wang ◽  
Guanrong Chen
Keyword(s):  
Dynamical Networks ◽  
Scale Free

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.

COMPLEX NETWORKS: TOPOLOGY, DYNAMICS AND SYNCHRONIZATION

2002 ◽  
Vol 12 (05) ◽  
pp. 885-916 ◽  
Author(s):  
XIAO FAN WANG
Keyword(s):  
Complex Networks ◽  
Network Models ◽  
Small World ◽  
Dynamical Networks ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
The Past ◽  
The Relationship

Dramatic advances in the field of complex networks have been witnessed in the past few years. This paper reviews some important results in this direction of rapidly evolving research, with emphasis on the relationship between the dynamics and the topology of complex networks. Basic quantities and typical examples of various complex networks are described; and main network models are introduced, including regular, random, small-world and scale-free models. The robustness of connectivity and the epidemic dynamics in complex networks are also evaluated. To that end, synchronization in various dynamical networks are discussed according to their regular, small-world and scale-free connections.

ON SYNCHRONIZABILITY OF DYNAMICAL LOCAL-WORLD NETWORKS

2008 ◽  
Vol 22 (17) ◽  
pp. 2713-2723 ◽  
Author(s):  
SHIWEN SUN ◽  
ZHONGXIN LIU ◽  
ZENGQIANG CHEN ◽  
ZHUZHI YUAN
Keyword(s):  
Dynamical Systems ◽  
Random Errors ◽  
Dynamical Networks ◽  
Scale Free ◽  
Node Removal ◽  
Exponential Networks

Synchronization phenomena in dynamical systems with local-world topologies are investigated. The effect of local-world size M on the synchronizability is studied. A larger M makes networks more synchronizable. Then the ability of dynamical networks to resist random errors and attacks is analyzed and compared with those of scale-free and exponential networks. Two attacking strategies are adopted, and a better quantity is used to measure the changes in synchronizability after node removal.

EFFECTS OF MOTION ON EPIDEMIC SPREADING

2010 ◽  
Vol 20 (03) ◽  
pp. 765-773 ◽  
Author(s):  
ARTURO BUSCARINO ◽  
AGNESE DI STEFANO ◽  
LUIGI FORTUNA ◽  
MATTIA FRASCA ◽  
VITO LATORA
Keyword(s):  
Mobile Agents ◽  
Small World ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Long Distance ◽  
Dynamical Networks ◽  
Scale Free ◽  
Random Walkers ◽  
Human Movements ◽  
Disease Spreading

The study of social networks, and in particular those aspects related to disease spreading, has recently attracted considerable attention in the scientific community. In this paper, we investigate the effect of motion on the spread of diseases in dynamical networks of mobile agents. In order to simulate the long distance displacements empirically observed in real human movements, we consider different motion rules, such as random walks with the addition of jumps or Lévy flights. We compare the epidemic thresholds found in dynamical networks of mobile agents with the analogous expressions for static networks. We discuss the existing relations between dynamical networks of random walkers with jumps and static small-world networks, and those between systems of Lévy walkers and scale-free networks.

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 .

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