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 H∞-Based Pinning Synchronization of General Complex Dynamical Networks with Coupling Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bowen Du ◽  
Dianfu Ma
Keyword(s):  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
External Disturbances ◽  
Dynamical Networks ◽  
Attenuation Index ◽  
General Complex ◽  
Local Feedback ◽  
Theoretical Results

This paper investigates the synchronization of complex dynamical networks with coupling delays and external disturbances by applying local feedback injections to a small fraction of nodes in the whole network. Based onH∞control theory, some delay-independent and -dependent synchronization criteria with a prescribedH∞disturbances attenuation index are derived for such controlled networks in terms of linear matrix inequalities (LMIs), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to reach network synchronization. A simulation example is included to validate the theoretical results.

scholarly journals Resilience of Interbank Market Networks to Shocks

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Shouwei Li ◽  
Jianmin He
Keyword(s):  
Network Models ◽  
Small World ◽  
Interbank Market ◽  
Small World Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Tiered Networks ◽  
The Stability ◽  
Random Shocks ◽  
Market Networks

This paper first constructs a tiered network model of the interbank market. Then, from the perspective of contagion risk, it studies numerically the resilience of four types of interbank market network models to shocks, namely, tiered networks, random networks, small-world networks, and scale-free networks. This paper studies the interbank market with homogeneous and heterogeneous banks and analyzes random shocks and selective shocks. The study reveals that tiered interbank market networks and random interbank market networks are basically more vulnerable against selective shocks, while small-world interbank market networks and scale-free interbank market networks are generally more vulnerable against random shocks. Besides, the results indicate that, in the four types of interbank market networks, scale-free networks have the highest stability against shocks, while small-world networks are the most vulnerable. When banks are homogeneous, faced with selective shocks, the stability of the tiered interbank market networks is slightly lower than that of random interbank market networks, whereas, in other cases, the stability of the tiered interbank market networks is basically between that of random interbank market networks and that of scale-free interbank market 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 .

PINNING IMPULSIVE SYNCHRONIZATION OF COMPLEX DYNAMICAL NETWORKS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250239 ◽  
Author(s):  
NARIMAN MAHDAVI ◽  
MOHAMMAD B. MENHAJ ◽  
JÜRGEN KURTHS ◽  
JIANQUAN LU ◽  
AHMAD AFSHAR
Keyword(s):  
Efficient Algorithm ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Dynamical Network ◽  
Impulsive Synchronization ◽  
Strongly Connected ◽  
Successful Control ◽  
The Relationship

In this paper, the problem of pinning impulsive synchronization for complex dynamical networks with directed or undirected but a strongly connected topology is investigated. To remedy this problem, we propose an efficient algorithm to find certain suitable nodes to be controlled via pinning and these selected nodes, in general, could be different at distinct impulsive time instants. The proposed algorithm guarantees the efficiency of the designed pinning impulsive strategy for the global exponential synchronization of state-coupled dynamical networks under an easily-verified condition. In other words, impulsive controllers and an efficient algorithm are designed to control a small fraction of the nodes, which successfully controls the whole dynamical network. Furthermore, we also estimate the upper bound of the number of pinning nodes, which is shown to be closely related to the impulsive intervals. The relationship implies that the required number of pinning nodes, which should be controlled for the successful control of the whole dynamical network, can be greatly reduced by reducing the impulses interval. Finally, simulations of scale-free and small-world networks are given to illustrate the effectiveness of the theoretical results.

Synchronization and Bifurcation of General Complex Dynamical Networks

2007 ◽  
Vol 47 (6) ◽  
pp. 1073-1075 ◽  
Author(s):  
Sun Wei-Gang ◽  
Xu Cong-Xiang ◽  
Li Chang-Pin ◽  
Fang Jin-Qing
Keyword(s):  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
General Complex

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.

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