Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2

Research Article

Epidemic Self-synchronization in Complex Networks

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  • @INPROCEEDINGS{10.1007/978-3-642-02469-6_56,
        author={Ingo Scholtes and Jean Botev and Markus Esch and Peter Sturm},
        title={Epidemic Self-synchronization in Complex Networks},
        proceedings={Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2},
        proceedings_a={COMPLEX PART 2},
        year={2012},
        month={5},
        keywords={Self-Synchronization Networks Coupled Oscillators Kuramoto Model Peer-to-Peer},
        doi={10.1007/978-3-642-02469-6_56}
    }
    
  • Ingo Scholtes
    Jean Botev
    Markus Esch
    Peter Sturm
    Year: 2012
    Epidemic Self-synchronization in Complex Networks
    COMPLEX PART 2
    Springer
    DOI: 10.1007/978-3-642-02469-6_56
Ingo Scholtes1,*, Jean Botev1, Markus Esch2,*, Peter Sturm1
  • 1: University of Trier
  • 2: University of Luxembourg
*Contact email: scholtes@syssoft.uni-trier.de, markus.esch@uni.lu

Abstract

In this article we present and evaluate an epidemic algorithm for the synchronization of coupled Kuramoto oscillators in complex network topologies. The algorithm addresses the problem of providing a global, synchronous notion of time in complex, dynamic Peer-to-Peer topologies. For this it requires a periodic coupling of nodes to a single random one-hop-neighbor. The strength of the nodes’ couplings is given as a function of the degrees of both coupling partners. We study the emergence of self-synchronization and the resilience against node failures for different coupling strength functions and network topologies. For Watts/Strogatz networks, we observe critical behavior suggesting that small-world properties of the underlying topology are crucial for self-synchronization to occur. From simulations on networks under the effect of churn, we draw the conclusion that special coupling functions can be used to enhance synchronization resilience in power-law Peer-to-Peer topologies.