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Journals

International Journal of Bifurcation and Chaos (IJBC)
 in Applied Sciences and Engineering

Volume: 22, Number: 7
http://www.worldscientific.com/worldscinet/ijbc

Theme Section: Complex Network Systems — From Theory To Applications

Editorial

R. Criado, M. Romance, Y. Moreno, J. Gómez-Gardeñes

Theme Section: Complex Network Systems — From Theory To Applications: Tutorials And Reviews

Unsupervised Clustering Analysis: A Multiscale Complex Networks Approach

Clara Granell, Sergio Gómez, Alex Arenas

Theme Section: Complex Network Systems — From Theory To Applications: Papers

Complex Networks Evolutionary Dynamics Using Genetic Algorithms

Daniel Aguilar-Hidalgo, Antonio Córdoba Zurita, Ma Carmen Lemos Fernández

Topological Versus Dynamical Robustness In A Lexical Network

Javier Borge-Holthoefer, Yamir Moreno, Alex Arenas

Redundancy In Functional Brain Connectivity From Eeg Recordings

Fabrizio De Vico Fallani, Jlenia Toppi, Claudia Di Lanzo, Giovanni Vecchiato, Laura Astolfi, Gianluca Borghini, Donatella Mattia, Febo Cincotti, Fabio Babiloni

Reliability Of Optimal Linear Projection Of Growing Scale-Free Networks

Pau Erola, Javier Borge-Holthoefer, Sergio Gomez, Alex Arenas

Detecting Series Periodicity With Horizontal Visibility Graphs

Angel Nuñez, Lucas Lacasa, Eusebio Valero, Jose Patricio Gómez, Bartolo Luque

Pacemakers In A Cayley Tree Of Kuramoto Oscillators

Pablo M. Gleiser, Luce Prignano, Conrad J. Pérez-Vicente, Albert Díaz-Guilera

A Model To Classify Users Of Social Networks Based On Pagerank

Francisco Pedroche

A Post-Processing Method For Interest Point Location In Images By Using Weighted Line-Graph Complex Networks

Regino Criado, Miguel Romance, Ángel Sánchez

Dynamics Of Persistent Infections In Homogeneous Populations

Joaquín Sanz, Luis Mario Floría, Yamir Moreno

Exploring The Kibble–Zurek Mechanism In A Secondary Bifurcation

M. A. Miranda, J. Burguete, W. González-Viñas, H. Mancini

Hybrid Recommendation Algorithm Based On Two Roles Of Social Tags

Zi-Ke Zhang, Chuang Liu

Theme Section: Dynamics And Processes Of Complex Networks

Editorial

M. Zanin, R. Gutiérrez, R. Bajo, J. M. Buldú, D. Papo, S. Boccaletti

Theme Section: Dynamics And Processes Of Complex Networks: Papers

Nonlocal Analysis Of Modular Roles

J. M. Buldú, I. Sendiña-Nadal, I. Leyva, J. A. Almendral, M. Zanin, S. Boccaletti

Adaptive Growing Networks Coevolving With The Spread Of Diseases

Beniamino Guerra, Jesús Gómez-Gardeñes, Vito Latora

Complex Dynamical Behaviors Of Deflection Routing On Grid Networks

Wilson Wang-Kit Thong, Guanrong Chen

Effects Of Traffic Properties And Degree Heterogeneity In Flow Fluctuations On Complex Networks

Sandro Meloni, Jesús Gómez-Gardeñes, Vito Latora, Yamir Moreno

Hierarchical Multiresolution Method To Overcome The Resolution Limit In Complex Networks

Clara Granell, Sergio Gómez, Alex Arenas

Saddle-Node Bifurcation Cascades And Associated Traveling Waves In Weakly Coupling Cml

Ma Dolores Sotelo Herrera, Jesús San Martín, Lucía Cerrada

Bifurcations In A Star-Like Network Of Stuart–Landau Oscillators

Mattia Frasca, André Bergner, Jürgen Kurths, Luigi Fortuna

Structure And Dynamics: The Transition From Nonequilibrium To Equilibrium In Integrate-And-Fire Dynamics

Cesar H. Comin, João L. B. Batista, Matheus P. Viana, Luciano Da F. Costa, Bruno A. N. Travençolo, Marcus Kaiser

Noise-Induced Up/Down Dynamics In Scale-Free Neuronal Networks

Jordi Grau-Moya, Antonio J. Pons, Jordi Garcia-Ojalvo

Pinning Impulsive Stabilization Of Nonlinear Dynamical Networks With Time-Varying Delay

Jianquan Lu, Zidong Wang, Jinde Cao, Daniel W.C. Ho, Jürgen Kurths

Targeting And Control Of Synchronization In Chaotic Oscillators

E. Padmanaban, Ranjib Banerjee, Shyamal Kumar Dana

Global And Partial Phase Synchronizations In Arrays Of Piecewise Linear Time-Delay Systems

R. Suresh, D. V. Senthilkumar, M. Lakshmanan, J. Kurths

Synchronization Of Moving Integrate And Fire Oscillators

Luce Prignano, Oleguer Sagarra, Pablo M. Gleiser, Albert Diaz-Guilera

Modeling The Evolution Of Item Rating Networks Using Time-Domain Preferential Attachment

Edmundo F. Lavia, Ariel Chernomoretz, Javier M. Buldú, Massimiliano Zanin, Pablo Balenzuela

Dependency Network And Node Influence: Application To The Study Of Financial Markets

Dror Y. Kenett, Tobias Preis, Gitit Gur-Gershgoren, Eshel Ben-Jacob
　

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Classical Papers
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An Extension Problem Related to the Fractional Laplacian

Luis Caffarellia & Luis Silvestre

Publication information: Luis Caffarellia & Luis Silvestre, An Extension Problem Related to the Fractional Laplacian. Communications in Partial Differential Equations, Volume 32 (8), 2007, 1245-1260. http://www.tandfonline.com/doi/abs/10.1080/03605300600987306

Abstract

The operator square root of the Laplacian (−Δ)^1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this article, we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.

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Fractional Laplacian in bounded domains

A. Zoia, A. Rosso and M. Kardar

Publication information: A.Zoia, A. Rosso and M. Kardar, Fractional Laplacian in bounded domains, Phys. Rev. E 76, 021116 (2007) [11 pages]. http://pre.aps.org/abstract/PRE/v76/i2/e021116

Abstract

The fractional Laplacian operator −(−Δ)^α∕2 appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely, hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalue spectrum are also obtained.

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Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency

W. Chen, S. Holm

Publication information: W. Chen, S. Holm, Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency, J. Acoust. Soc. Am. 115 (4), 2004, 1424–1430. http://asadl.org/jasa/resource/1/jasman/v115/i4/p1424_s1?isAuthorized=no

Abstract

Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo's smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.

Free download link:  http://em.hhu.edu.cn/chenwen/papers/softmatter/JASA_space.pdf

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