Concurrent enhancement of percolation and synchronization in adaptive networks

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems’ collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems.

[1]  Jianye Zhao,et al.  Adaptive coupling and enhanced synchronization in coupled phase oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[3]  Michele Catanzaro,et al.  Dynamical processes in complex networks , 2008 .

[4]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[5]  Albert-László Barabási,et al.  Scale-free networks , 2008, Scholarpedia.

[6]  Changsong Zhou,et al.  Dynamical weights and enhanced synchronization in adaptive complex networks. , 2006, Physical review letters.

[7]  Toshio Aoyagi,et al.  Co-evolution of phases and connection strengths in a network of phase oscillators. , 2009, Physical review letters.

[8]  J Gómez-Gardeñes,et al.  Emerging meso- and macroscales from synchronization of adaptive networks. , 2011, Physical review letters.

[9]  Toshio Aoyagi,et al.  Self-organized network of phase oscillators coupled by activity-dependent interactions. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Jennifer L. Glanville,et al.  BIRDS OF A FEATHER : Homophily in Social Networks , 2014 .

[11]  F. C. Santos,et al.  Evolutionary games in self-organizing populations , 2008 .

[12]  Guido Caldarelli,et al.  Self-organized network evolution coupled to extremal dynamics , 2008 .

[13]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[14]  J. Spencer,et al.  Explosive Percolation in Random Networks , 2009, Science.

[15]  J. Kurths,et al.  Synchronization in networks of mobile oscillators. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Sergio Gómez,et al.  Explosive synchronization transitions in scale-free networks. , 2011, Physical review letters.

[17]  Martin Hasler,et al.  Dynamics of Stochastically Blinking Systems. Part I: Finite Time Properties , 2013, SIAM J. Appl. Dyn. Syst..

[18]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

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

[20]  L Prignano,et al.  Tuning synchronization of integrate-and-fire oscillators through mobility. , 2013, Physical review letters.

[21]  M. Barthelemy,et al.  Microdynamics in stationary complex networks , 2008, Proceedings of the National Academy of Sciences.

[22]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[23]  Vito Latora,et al.  Emergence of structural patterns out of synchronization in networks with competitive interactions , 2011, Scientific reports.

[24]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2005, IEEE Transactions on Automatic Control.

[25]  Diego Garlaschelli,et al.  Fitness-dependent topological properties of the world trade web. , 2004, Physical review letters.

[26]  S. Boccaletti,et al.  Synchronization is enhanced in weighted complex networks. , 2005, Physical review letters.

[27]  E. Ott,et al.  Adaptive synchronization of dynamics on evolving complex networks. , 2008, Physical review letters.

[28]  Adilson E Motter,et al.  Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? , 2003, Physical review letters.

[29]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[30]  Alex Arenas,et al.  Paths to synchronization on complex networks. , 2006, Physical review letters.

[31]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[32]  Francesco Sorrentino.  Adaptive coupling for achieving stable synchronization of chaos. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Thilo Gross,et al.  Adaptive Networks: Theory, Models and Applications , 2009 .

[34]  M. Hasler,et al.  Blinking model and synchronization in small-world networks with a time-varying coupling , 2004 .

[35]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[36]  Thilo Gross,et al.  Adaptive coevolutionary networks: a review , 2007, Journal of The Royal Society Interface.

[37]  Uta Dresdner,et al.  Chemical Oscillations Waves And Turbulence , 2016 .

[38]  Sang Hoon Lee,et al.  Phase-shift inversion in oscillator systems with periodically switching couplings. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[40]  L. G. Morelli,et al.  Dynamics of mobile coupled phase oscillators , 2013 .

[41]  Martin Hasler,et al.  Dynamics of Stochastically Blinking Systems. Part II: Asymptotic Properties , 2013, SIAM J. Appl. Dyn. Syst..

[42]  Beom Jun Kim,et al.  Factors that predict better synchronizability on complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Sudeshna Sinha,et al.  Synchronization in time-varying networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Zonghua Liu,et al.  Explosive synchronization in adaptive and multilayer networks. , 2014, Physical review letters.

[45]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[46]  S. Boccaletti,et al.  Synchronization of moving chaotic agents. , 2008, Physical review letters.