Pinning control of scale-free dynamical networks

2002 ◽  
Vol 310 (3-4) ◽  
pp. 521-531 ◽  
Author(s):  
Xiao Fan Wang ◽  
Guanrong Chen
Keyword(s):  
Pinning Control ◽  
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.

scholarly journals Pinning synchronization of the drive and response dynamical networks with lag

2014 ◽  
Vol 24 (3) ◽  
pp. 257-270 ◽  
Author(s):  
Bohui Wen ◽  
Mo Zhao ◽  
Fanyu Meng
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Schur Complement ◽  
Pinning Control ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
General Complex ◽  
Minimum Number

Abstract This paper investigates the pinning synchronization of two general complex dynamical networks with lag. The coupling configuration matrices in the two networks are not need to be symmetric or irreducible. Several convenient and useful criteria for lag synchronization are obtained based on the lemma of Schur complement and the Lyapunov stability theory. Especially, the minimum number of controllers in pinning control can be easily obtained. At last, numerical simulations are provided to verify the effectiveness of the criteria

Decentralized Adaptive Pinning Control for Cluster Synchronization of Complex Dynamical Networks

2013 ◽  
Vol 43 (1) ◽  
pp. 394-399 ◽  
Author(s):  
Housheng Su ◽  
Zhihai Rong ◽  
Michael Z. Q. Chen ◽  
Xiaofan Wang ◽  
Guanrong Chen ◽  
...  
Keyword(s):  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Cluster Synchronization ◽  
Dynamical Networks

scholarly journals Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fang-Di Kong
Keyword(s):  
Time Scales ◽  
Discrete Time ◽  
Control Strategy ◽  
Continuous Time ◽  
General Framework ◽  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Synchronization Problem

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

THE EFFECT OF PINNING CONTROL ON EVOLUTIONARY PRISONER'S DILEMMA GAME

2010 ◽  
Vol 24 (25) ◽  
pp. 2581-2589 ◽  
Author(s):  
WEN-BO DU ◽  
HONG ZHOU ◽  
ZHEN LIU ◽  
XIAN-BIN CAO
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Pinning Control ◽  
Control Mechanisms ◽  
Control Cost ◽  
Prisoner’S Dilemma Game ◽  
Scale Free ◽  
Prisoner's Dilemma Game ◽  
Control Degree

The evolutionary game on graphs provides a natural framework to investigate the cooperation behavior existing in natural and social society. In this paper, degree-based pinning control and random pinning control are introduced into the evolutionary prisoner's dilemma game on scale-free networks, and the effects of control mechanism and control cost on the evolution are studied. Numerical simulation shows that forcing some nodes to cooperate (defect) will increase (decrease) the frequency of cooperators. Compared with random pinning control, degree-based pinning control is more efficient, and degree-based pinning control costs less than random pinning control to achieve the same goal. Numerical results also reveal that the evolutionary time series is more stable under pinning control mechanisms, especially under the degree-based pinning control.

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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