Image Entropy for the Identification of Chimera States of Spatiotemporal Divergence in Complex Coupled Maps of Matrices

Complex networks of coupled maps of matrices (NCMM) are investigated in this paper. It is shown that a NCMM can evolve into two different steady states—the quiet state or the state of divergence. It appears that chimera states of spatiotemporal divergence do exist in the regions around the boundary lines separating these two steady states. It is demonstrated that digital image entropy can be used as an effective measure for the visualization of these regions of chimera states in different networks (regular, feed-forward, random, and small-world NCMM).

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Networks

10.1093/oso/9780198821939.003.0004 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Complex Systems ◽

Complex Networks ◽

Phase Diagrams ◽

Community Detection ◽

Network Science ◽

Small World ◽

Small World Networks ◽

Multilayer Networks ◽

Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

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Small world in a seismic network: the California case

Nonlinear Processes in Geophysics ◽

10.5194/npg-15-389-2008 ◽

2008 ◽

Vol 15 (3) ◽

pp. 389-395 ◽

Cited By ~ 21

Author(s):

A. Jiménez ◽

K. F. Tiampo ◽

A. M. Posadas

Keyword(s):

Complex Networks ◽

Recent Work ◽

Brain Activity ◽

Social Systems ◽

Small World ◽

Functional Networks ◽

Topological Properties ◽

Southern California Region ◽

Seismic Area ◽

The Brain

Abstract. Recent work has shown that disparate systems can be described as complex networks i.e. assemblies of nodes and links with nontrivial topological properties. Examples include technological, biological and social systems. Among them, earthquakes have been studied from this perspective. In the present work, we divide the Southern California region into cells of 0.1°, and calculate the correlation of activity between them to create functional networks for that seismic area, in the same way that the brain activity is studied from the complex network perspective. We found that the network shows small world features.

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Sizing complex networks

Communications Physics ◽

10.1038/s42005-019-0239-0 ◽

2019 ◽

Vol 2 (1) ◽

Cited By ~ 2

Author(s):

Gorka Zamora-López ◽

Romain Brasselet

Keyword(s):

Complex Networks ◽

Random Graphs ◽

Null Model ◽

Small World ◽

Small World Network ◽

The Many

AbstractAmong the many features of natural and man-made complex networks the small-world phenomenon is a relevant and popular one. But, how small is a small-world network and how does it compare to others? Despite its importance, a reliable and comparable quantification of the average pathlength of networks has remained an open challenge over the years. Here, we uncover the upper (ultra-long (UL)) and the lower (ultra-short (US)) limits for the pathlength and efficiency of networks. These results allow us to frame their length under a natural reference and to provide a synoptic representation, without the need to rely on the choice for a null-model (e.g., random graphs or ring lattices). Application to empirical examples of three categories (neural, social and transportation) shows that, while most real networks display a pathlength comparable to that of random graphs, when contrasted against the boundaries, only the cortical connectomes prove to be ultra-short.

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COMPLEX NETWORKS: TOPOLOGY, DYNAMICS AND SYNCHRONIZATION

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402004802 ◽

2002 ◽

Vol 12 (05) ◽

pp. 885-916 ◽

Cited By ~ 397

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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TRAFFIC CONGESTION ANALYSIS IN COMPLEX NETWORKS BASED ON VARIOUS ROUTING STRATEGIES

Modern Physics Letters B ◽

10.1142/s0217984907013389 ◽

2007 ◽

Vol 21 (15) ◽

pp. 929-939 ◽

Cited By ~ 4

Author(s):

XUAN GUO ◽

HONGTAO LU

Keyword(s):

Complex Networks ◽

Traffic Congestion ◽

Small World ◽

Modern Society ◽

Information Communication ◽

Shortest Path Routing ◽

Scale Free ◽

Deterministic Routing ◽

Routing Strategy ◽

Network Topologies

Networks, acting as infrastructure for information communication, play an important role in modern society, therefore, the elements affecting the efficiency of network traffic are worthy of deep research. In this paper, we investigate numerically the problem of traffic congestion in complex networks through the use of various routing strategies. Three types of complex networks structures, namely Poisson random networks, small-world networks and scale-free networks, are considered. Three different routing strategies are used on networks: deterministic routing strategy, preferential routing strategy and shortest path routing strategy. We evaluate the efficiency of different routing strategies on different network topologies and show how the network structures and routing strategies influence the traffic congestion status.

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Chimera states in time-varying complex networks

Physical Review E ◽

10.1103/physreve.91.022817 ◽

2015 ◽

Vol 91 (2) ◽

Cited By ~ 61

Author(s):

Arturo Buscarino ◽

Mattia Frasca ◽

Lucia Valentina Gambuzza ◽

Philipp Hövel

Keyword(s):

Complex Networks ◽

Time Varying ◽

Chimera States

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STEADY STATES OF EPIDEMIC SPREADING IN SMALL-WORLD NETWORKS

International Journal of Modern Physics C ◽

10.1142/s0129183104006881 ◽

2004 ◽

Vol 15 (10) ◽

pp. 1471-1477 ◽

Cited By ~ 4

Author(s):

XIN-JIAN XU ◽

ZHI-XI WU ◽

YONG CHEN ◽

YING-HAI WANG

Keyword(s):

Analytical Methods ◽

Large Scale ◽

Small World ◽

Spreading Rate ◽

Steady States ◽

Critical Threshold ◽

Small World Networks ◽

Epidemic Spreading ◽

Sis Model ◽

Large Scale Simulations

We consider a standard susceptible–infected–susceptible (SIS) model to study the behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual epidemic behavior with a critical threshold λc below which infectious diseases die out. For the spreading rate λ far above λc, it was found that the density of infected individuals ρ as a function of λ has the property ρ≈f(K)( ln λ- ln λc).

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Propagation and stability in software: A complex network perspective

International Journal of Modern Physics C ◽

10.1142/s0129183115500527 ◽

2015 ◽

Vol 26 (05) ◽

pp. 1550052 ◽

Cited By ~ 6

Author(s):

Lei Wang ◽

Ping Wang

Keyword(s):

Software Engineering ◽

Complex Networks ◽

Large Scale ◽

Structural Difference ◽

Small World ◽

Change Propagation ◽

Small World Networks ◽

Typical Structure ◽

Scale Free ◽

Scale Free Networks

In this paper, we attempt to understand the propagation and stability feature of large-scale complex software from the perspective of complex networks. Specifically, we introduced the concept of "propagation scope" to investigate the problem of change propagation in complex software. Although many complex software networks exhibit clear "small-world" and "scale-free" features, we found that the propagation scope of complex software networks is much lower than that of small-world networks and scale-free networks. Furthermore, because the design of complex software always obeys the principles of software engineering, we introduced the concept of "edge instability" to quantify the structural difference among complex software networks, small-world networks and scale-free networks. We discovered that the edge instability distribution of complex software networks is different from that of small-world networks and scale-free networks. We also found a typical structure that contributes to the edge instability distribution of complex software networks. Finally, we uncovered the correlation between propagation scope and edge instability in complex networks by eliminating the edges with different instability ranges.

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