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Broad-scale small-world network topology induces optimal synchronization of flexible oscillators

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  • Markovič, Rene
  • Gosak, Marko
  • Marhl, Marko

Abstract

The discovery of small-world and scale-free properties of many man-made and natural complex networks has attracted increasing attention. Of particular interest is how the structural properties of a network facilitate and constrain its dynamical behavior. In this paper we study the synchronization of weakly coupled limit-cycle oscillators in dependence on the network topology as well as the dynamical features of individual oscillators. We show that flexible oscillators, characterized by near zero values of divergence, express maximal correlation in broad-scale small-world networks, whereas the non-flexible (rigid) oscillators are best correlated in more heterogeneous scale-free networks. We found that the synchronization behavior is governed by the interplay between the networks global efficiency and the mutual frequency adaptation. The latter differs for flexible and rigid oscillators. The results are discussed in terms of evolutionary advantages of broad-scale small-world networks in biological systems.

Suggested Citation

  • Markovič, Rene & Gosak, Marko & Marhl, Marko, 2014. "Broad-scale small-world network topology induces optimal synchronization of flexible oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 14-21.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:14-21
    DOI: 10.1016/j.chaos.2014.08.008
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    References listed on IDEAS

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    5. Gosak, Marko & Markovič, Rene & Marhl, Marko, 2012. "The role of neural architecture and the speed of signal propagation in the process of synchronization of bursting neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2764-2770.
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    Cited by:

    1. Soriano-Sánchez, A.G. & Posadas-Castillo, C., 2018. "Smart pattern to generate small–world networks," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 415-422.
    2. Dobovišek, Andrej & Markovič, Rene & Brumen, Milan & Fajmut, Aleš, 2018. "The maximum entropy production and maximum Shannon information entropy in enzyme kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 220-232.

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