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Excitation waves on a minimal small-world model

  • Thomas Isele
  • Benedikt Hartung
  • Philipp HövelEmail author
  • Eckehard Schöll
Regular Article

Abstract

We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of spatio-temporal behavior that is not present without it. We describe the underlying mechanisms for different types of patterns: propagation failure, period decreasing, bistability, shortcut blocking and period multiplication. For this purpose, we investigate the dependence on d, the network size, the coupling range in the original ring and the global coupling strength and present a phase diagram summarizing the different scenarios. Furthermore, we discuss the scaling behavior of the critical distance by analytical means and address the connection to spatially continuous excitable media.

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Thomas Isele
    • 1
  • Benedikt Hartung
    • 1
  • Philipp Hövel
    • 1
    • 2
    Email author
  • Eckehard Schöll
    • 1
  1. 1.Institut für Theoretische Physik, Technische Universität BerlinBerlinGermany
  2. 2.Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu BerlinBerlinGermany

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