Increasing synchronizability in a scale-free network via edge elimination

Abstract In this paper, synchronization of a Scale-Free (SF) network of chaotic oscillators is addressed. Synchronizability is increased, while eliminating edges in a SF network. We propose two novel methods using perturbation theory as an edge selection criteria, to eliminate the least amount of edges. Also we modified one existing method from the literature. These methods yielded the best results at increasing synchronizability the most per edge eliminated, while avoiding node isolation. These three strategies were tested in SF networks with different average degrees, and compared with other five strategies found in literature. Some five criterions on the selection of the method are given. This paper is especially interested in Case 3 of the Master Stability Function, which allows synchronizability to be defined. Therefore we use chaotic Rossler oscillators as nodes in the SF networks.

[1]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[2]  Guido Caldarelli,et al.  Preferential attachment in the growth of social networks: the case of Wikipedia , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Sergio Gomez Colmenarejo,et al.  Hybrid computing using a neural network with dynamic external memory , 2016, Nature.

[4]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[5]  C. Kadushin.  Understanding Social Networks: Theories, Concepts, and Findings , 2011 .

[6]  César Cruz-Hernández,et al.  Coupling strength computation for chaotic synchronization of complex networks with multi-scroll attractors , 2016, Appl. Math. Comput..

[7]  A. G. Soriano-Sánchez,et al.  Smart pattern to generate small–world networks , 2018 .

[8]  R. Guimerà,et al.  The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[9]  S. Simard,et al.  Mycorrhizal networks: Mechanisms, ecology and modelling , 2012 .

[10]  Roger Chiu,et al.  Discrete-time neural synchronization between an Arduino microcontroller and a Compact Development System using multiscroll chaotic signals , 2019, Chaos, Solitons & Fractals.

[11]  A. Barabasi,et al.  Scale-free characteristics of random networks: the topology of the world-wide web , 2000 .

[12]  Emilio Hernández-García,et al.  Wikipedia Information Flow Analysis Reveals the Scale-Free Architecture of the Semantic Space , 2011, PloS one.

[13]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[14]  S. Bornholdt,et al.  Scale-free topology of e-mail networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Jinde Cao,et al.  Pinning synchronization of linearly coupled delayed neural networks , 2012, Math. Comput. Simul..

[16]  A. Hagberg,et al.  Rewiring networks for synchronization. , 2008, Chaos.

[17]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .

[18]  C. Cruz-Hernández,,et al.  Communicating encrypted information based on synchronized hyperchaotic maps , 2010 .

[19]  César Cruz-Hernández,et al.  Chaotic synchronization of irregular complex network with hysteretic circuit-like oscillators in hamiltonian form and its application in private communications , 2016 .

[20]  I Leyva,et al.  Regulating synchronous states of complex networks by pinning interaction with an external node. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[22]  Beom Jun Kim,et al.  Attack vulnerability of complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[24]  Abdelkrim Boukabou,et al.  Generalized chaos control and synchronization by nonlinear high-order approach , 2012, Math. Comput. Simul..

[25]  P. Halmos.  What Does the Spectral Theorem Say , 1963 .

[26]  Monica L. Mo,et al.  Global reconstruction of the human metabolic network based on genomic and bibliomic data , 2007, Proceedings of the National Academy of Sciences.

[27]  Xiao Fan Wang,et al.  Complex Networks: Topology, Dynamics and Synchronization , 2002, Int. J. Bifurc. Chaos.

[28]  Chao Liu,et al.  Are networks with more edges easier to synchronize? , 2007, ArXiv.