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.

HYPERCHAOTIC SYNCHRONIZATION IN DETERMINISTIC SMALL-WORLD DYNAMICAL NETWORKS

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2674-2679 ◽  
Author(s):  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
SHOU-LIANG BU ◽  
QING-HUA XIA ◽  
XIAO-SHU LUO
Keyword(s):  
Complex Networks ◽  
Continuous Time ◽  
Weak Coupling ◽  
Nearest Neighbor ◽  
Small World ◽  
Feedback System ◽  
Small World Network ◽  
Single Node ◽  
Hyperchaotic Synchronization ◽  
Real Complex

In this paper, hyperchaotic synchronization in a network of continuous-time dynamical systems with small-world connections is investigated. The small-world network is obtained by selecting a part of nodes to be hubs and then using a globally coupled network to interconnect these hubs in an originally nearest-neighbor coupled network. We show that, the deterministic small-world dynamical network will also synchronize when the maximal Lyapunov exponent of the self-feedback system of single node is equated to, even great than zero. This explains why many real-world complex networks exhibit strong tendency toward synchronization even with a relatively weak coupling. Our study may shed some new light on synchronization phenomena in real complex networks.

A NOVEL SMALL-WORLD NETWORK MODEL: KEEPING CONNECTIVITY WITHOUT ADDING EDGES

2008 ◽  
Vol 22 (29) ◽  
pp. 5229-5234 ◽  
Author(s):  
XUHUA YANG ◽  
BO WANG ◽  
WANLIANG WANG ◽  
YOUXIAN SUN
Keyword(s):  
Network Model ◽  
Regular Ring ◽  
Nearest Neighbor ◽  
Small World ◽  
Clustering Coefficient ◽  
The Novel ◽  
Small World Network ◽  
Characteristic Path Length ◽  
Large N ◽  
Novel Model

Considering the problems of potentially generating a disconnected network in the WS small-world network model [Watts and Strogatz, Nature393, 440 (1998)] and of adding edges in the NW small-world network model [Newman and Watts, Phys. Lett. A263, 341 (1999)], we propose a novel small-world network model. First, generate a regular ring lattice of N vertices. Second, randomly rewire each edge of the lattice with probability p. During the random rewiring procedure, keep the edges between the two nearest neighbor vertices, namely, always keep a connected ring. This model need not add edges and can maintain connectivity of the network at all times in the random rewiring procedure. Simulation results show that the novel model has the typical small-world properties which are small characteristic path length and high clustering coefficient. For large N, the model is approximately equal to the WS model. For large N and small p, the model is approximately equal to the WS model or the NW model.

Synchronization and rhythm dynamics of a neuronal network consisting of mixed bursting neurons with hybrid synapses

2016 ◽  
Vol 30 (16) ◽  
pp. 1650091 ◽  
Author(s):  
Xia Shi ◽  
Wenqi Xi
Keyword(s):  
Neuronal Network ◽  
Coupling Strength ◽  
Small World ◽  
Inhibitory Synapses ◽  
Small World Network ◽  
Average Width ◽  
Bursting Neurons ◽  
Burst Synchronization ◽  
Chemical Synapses ◽  
Width Factor

In this paper, burst synchronization and rhythm dynamics of a small-world neuronal network consisting of mixed bursting types of neurons coupled via inhibitory–excitatory chemical synapses are explored. Two quantities, the synchronization parameter and average width factor, are used to characterize the synchronization degree and rhythm dynamics of the neuronal network. Numerical results show that the percentage of the inhibitory synapses in the network is the major factor for we get a similarly bell-shaped dependence of synchronization on it, and the decrease of the average width factor of the network. We also find that not only the value of the coupling strength can promote the synchronization degree, but the probability of random edges adding to the small-world network also can. The ratio of the long bursting neurons has little effect on the burst synchronization and rhythm dynamics of the network.

THE INTERPLAY OF UNCORRELATED NOISE AND SMALL WORLD EFFECT ON PATTERN FORMATION IN TWO-DIMENSIONAL COUPLED MAP LATTICES

2012 ◽  
Vol 26 (31) ◽  
pp. 1250130 ◽  
Author(s):  
DAOGUANG WANG ◽  
XIAOSHA KANG ◽  
HUAPING LÜ
Keyword(s):  
Pattern Formation ◽  
Coupling Strength ◽  
Gaussian Noise ◽  
Nearest Neighbor ◽  
Spiral Wave ◽  
Small World ◽  
Coupled Map Lattices ◽  
Two Dimensional ◽  
Excitable Systems ◽  
Generic Dynamics

By using a neuron-like map model to denote the generic dynamics of excitable systems, Gaussian-noise-induced pattern formation in the two-dimensional coupled map lattices with nearest-neighbor coupling and shortcut links has been studied. Given the appropriate initial values and parameter regions, with all nodes concerned, the functions of δ(n), χ and ℜ are introduced to analyze the evolution of pattern formation. It is found that there exists a critical εc beyond which the stable rotating spiral wave will appear. After introducing the Gaussian noise for the homogeneous ε region, different spatiotemporal stable patterns will be achieved. Additionally, the importance of the parameter I on the coupling strength C is discussed.

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.

NEOCORTEX'S SMALL WORLD OF FRACTAL COUPLING

2007 ◽  
Vol 17 (10) ◽  
pp. 3409-3414 ◽  
Author(s):  
C. WAGNER ◽  
R. STOOP
Keyword(s):  
Analytical Approach ◽  
Probability Function ◽  
Nearest Neighbor ◽  
Small World ◽  
Small World Network ◽  
Information Propagation ◽  
Network Characteristics ◽  
Connectivity Probability ◽  
Neocortical Neurons ◽  
High Level

Biological neocortical neurons are arranged in a columnar clustered architecture. Using a mathematical model in which the clustering properties can be monitored by means of a connectivity probability function, we investigate the information propagation in the associated networks, by means of simulations and a semi-analytical approach. Our analysis demonstrates that for systems with n-nearest neighbor coupling, the information propagation increases linearly in the neighbor order n. For fractal coupling, shown to give rise to small-world network characteristics, in contrast, an enhanced dependence is found, that, in our model of the neocortex, quickly saturates at a high level, indicating the superiority of this network type.

scholarly journals Enhancing Controllability Robustness of q-Snapback Networks through Redirecting Edges

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Yang Lou ◽  
Lin Wang ◽  
Guanrong Chen
Keyword(s):  
Numerical Simulations ◽  
Network Model ◽  
Nearest Neighbor ◽  
Small World ◽  
Small World Network ◽  
Edge Removal ◽  
Regular Network ◽  
Node Removal ◽  
Network Controllability

The well-known small-world network model was established by randomly rewiring edges, aiming to enhance the synchronizability of an undirected nearest-neighbor regular network. This paper demonstrates via extensive numerical simulations that randomly redirecting edges could enhance the robustness of the network controllability for directed snapback networks against both random and intentional node-removal and edge-removal attacks.

The optimal synchronizability of complex networks with saturated coupling strength

2020 ◽  
Vol 31 (10) ◽  
pp. 2050139
Author(s):  
Chen Huang ◽  
Xinbiao Lu ◽  
Jun Zhou ◽  
Buzhi Qin
Keyword(s):  
Genetic Algorithm ◽  
Global Optimization ◽  
Network Topology ◽  
Coupling Strength ◽  
Small World ◽  
Pso Algorithm ◽  
Small World Network ◽  
Swarm Optimization ◽  
Edge Betweenness ◽  
Simulation Results

For networks with fixed network topology, when the total coupling strength between nodes is limited and the coupling strength between nodes is saturated, the global optimization algorithms including genetic algorithm (GA) and particle swarm optimization (PSO) algorithm are used to adjust the coupling strength between nodes to improve the synchronizability of the network, respectively. Simulation results show that in WS small-world network, when the edge betweenness centrality of the edge is large, the coupling strength of the edge after optimization is greater. Furthermore, compared with GA, PSO has better performance.

TIME-DELAY ROBUSTNESS OF CONSENSUS PROBLEMS IN REGULAR AND COMPLEX NETWORKS

2007 ◽  
Vol 18 (08) ◽  
pp. 1339-1350 ◽  
Author(s):  
ZHENGPING WU ◽  
ZHI-HONG GUAN
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Nearest Neighbor ◽  
Small World ◽  
Node Degree ◽  
Small World Network ◽  
Scale Free Network ◽  
Star Network ◽  
Scale Free ◽  
Free Network

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.

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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