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.

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 The use of the power law for designing wireless networks

2018 ◽  
Vol 21 ◽  
pp. 00012
Author(s):  
Andrzej Paszkiewicz
Keyword(s):  
Wireless Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Limited Resources ◽  
Random Networks ◽  
New Approach ◽  
Available Bandwidth ◽  
Scale Free ◽  
Scale Free Networks ◽  
Node Removal

The paper concerns the use of the scale-free networks theory and the power law in designing wireless networks. An approach based on generating random networks as well as on the classic Barabási-Albert algorithm were presented. The paper presents a new approach taking the limited resources for wireless networks into account, such as available bandwidth. In addition, thanks to the introduction of opportunities for dynamic node removal it was possible to realign processes occurring in wireless networks. After introduction of these modifications, the obtained results were analyzed in terms of a power law and the degree distribution of each node.

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.

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.

scholarly journals Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems

2007 ◽  
Vol 5 (25) ◽  
pp. 865-871 ◽  
Author(s):  
Alan Wilson
Keyword(s):  
Dynamical Systems ◽  
Statistical Physics ◽  
Spatial Interaction ◽  
Structural Evolution ◽  
Ecological Models ◽  
Similar Argument ◽  
Scale Free ◽  
Integrated Methodology ◽  
Scale Free Networks ◽  
Modelling Methodology

It is shown that Boltzmann's methods from statistical physics can be applied to a much wider range of systems, and in a variety of disciplines, than has been commonly recognized. A similar argument can be applied to the ecological models of Lotka and Volterra. Furthermore, it is shown that the two methodologies can be applied in combination to generate the Boltzmann, Lotka and Volterra (BLV) models. These techniques enable both spatial interaction and spatial structural evolution to be modelled, and it is argued that they potentially provide a much richer modelling methodology than that currently used in the analysis of ‘scale-free’ networks.

Statistical Selection of Relevant Features to Classify Random, Scale Free and Exponential Networks

2007 ◽  
pp. 454-461
Author(s):  
Laura Cruz Reyes ◽  
Eustorgio Meza Conde ◽  
Tania Turrubiates López ◽  
Claudia Guadalupe Gómez Santillán ◽  
Rogelio Ortega Izaguirre
Keyword(s):  
Scale Free ◽  
Statistical Selection ◽  
Random Scale ◽  
Exponential Networks ◽  
Selection Of

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.

QUANTIFYING LOCAL INSTABILITY AND PREDICTABILITY OF CHAOTIC DYNAMICAL SYSTEMS BY MEANS OF LOCAL METRIC ENTROPY

2000 ◽  
Vol 10 (01) ◽  
pp. 135-154 ◽  
Author(s):  
MOZHENG WEI
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Time Scales ◽  
Growth Rates ◽  
Metric Entropy ◽  
Random Errors ◽  
Local Instability ◽  
Instability Index ◽  
Local Growth ◽  
Chaotic Dynamical Systems

A local metric entropy (LME) is introduced and used as a measure of local instability of chaotic dynamical systems. The predictability time scale of a dynamical system during a given period of time can also be estimated with high accuracy by using the LME. It is shown that LME, at any time during the evolution of a dynamical system, can be calculated as the sum of all the positive local Lyapunov exponents (LEs). This conclusion implies that the positive local LEs represent the rates of local information changes along the directions of their respective Lyapunov vectors. LME does not depend upon the amplitudes nor the configurations of initial perturbations; it depends on the positive local LEs which are intrinsic properties of dynamical systems. In addition, the sum of all the local LEs is proven to be equal to the divergence of phase space. Thus for a general chaotic system at any time, the sum of all the local LEs is equal to the sum of all the local growth rates of either instantaneous optimal modes or normal modes. In analyzing local instability, the performance of LME is evaluated by comparing an instability index with LME, the first local LE, locally largest LE, local growth rates of the dominant instantaneous optimal mode and normal mode. When LME is used to estimate the predictability time scales of systems over specified time periods, it is found that the time scales defined by LME are generally closer to the standard predictability times than the Lyapunov times and Kolmogorov–Sinai times for most cases in the two dynamical systems we have tested. Both the instability index and standard predictability time are defined and calculated through a large number of random errors.

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