Cluster Mixed Synchronization of Complex Networks with Disturbance

2015 ◽  
Vol 719-720 ◽  
pp. 448-451
Author(s):  
Li Jie Zeng
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Bounded Disturbances ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, we investigate the cluster mixed synchronization scheme in time-varying delays coupled complex dynamical networks with disturbance. Basing on the community structure of the networks, some sufficient criteria are derived to ensure cluster mixed synchronization of the network model. Particularly, unknown bounded disturbances can be conquered by the proposed control. The numerical simulations are performed to verify the effectiveness of the theoretical results

scholarly journals Cluster Synchronization of Time-Varying Delays Coupled Complex Networks with Nonidentical Dynamical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shuguo Wang ◽  
Hongxing Yao ◽  
Mingping Sun
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Cluster Synchronization ◽  
Time Varying ◽  
Dynamical Networks ◽  
Synchronization Scheme ◽  
Theoretical Results

This paper investigates a new cluster synchronization scheme in the nonlinear coupled complex dynamical networks with nonidentical nodes. The controllers are designed based on the community structure of the networks; some sufficient criteria are derived to ensure cluster synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be symmetric, irreducible. The numerical simulations are performed to verify the effectiveness of the theoretical results.

scholarly journals Cluster Anti-Synchronization of Complex Networks with Nonidentical Dynamical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shuguo Wang ◽  
Chunyuan He ◽  
Hongxing Yao
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Numerical Simulations ◽  
Network Model ◽  
Complex Dynamical Networks ◽  
Time Varying ◽  
Dynamical Networks ◽  
Nonidentical Nodes ◽  
Theoretical Results

This paper investigates a new cluster antisynchronization scheme in the time-varying delays coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controllers are designed differently between the nodes in one community that have direct connections to the nodes in other communities and the nodes without direct connections with the nodes in other communities strategy; some sufficient criteria are derived to ensure cluster anti-synchronization of the network model. Particularly, the weight configuration matrix is not assumed to be irreducible. The numerical simulations are performed to verify the effectiveness of 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 Adaptive Exponential Synchronization of Coupled Complex Networks on General Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Song Liu ◽  
Xianfeng Zhou ◽  
Wei Jiang ◽  
Yizheng Fan
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Weighted Graph ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Exponential Rate ◽  
General Graphs ◽  
Theoretical Results ◽  
Variable Coupling

We investigate the synchronization in complex dynamical networks, where the coupling configuration corresponds to a weighted graph. An adaptive synchronization method on general coupling configuration graphs is given. The networks may synchronize at an arbitrarily given exponential rate by enhancing the updated law of the variable coupling strength and achieve synchronization more quickly by adding edges to original graphs. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results.

CHAOS GENERATION FOR A CLASS OF NONLINEAR COMPLEX NETWORKS

2013 ◽  
Vol 23 (02) ◽  
pp. 1350018 ◽  
Author(s):  
NA LIU ◽  
JUAN LI ◽  
ZHI-HONG GUAN ◽  
LI DING ◽  
GUILIN ZHENG
Keyword(s):  
Lyapunov Exponent ◽  
Complex Networks ◽  
Mathematical Analysis ◽  
Research Topic ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Example ◽  
Emergence Of Chaos ◽  
New Criteria ◽  
Theoretical Results

Chaos generation is an interesting research topic in the study of coupled complex dynamical networks. In this paper, based on mathematical analysis of Lyapunov exponent and boundedness of networks, the emergence of chaos for a class of nonlinear complex networks is investigated and some new criteria of chaos generation are derived. The effectiveness of theoretical results is verified by a numerical example.

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 Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

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