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Control of Desynchronization Transitions in Delay-Coupled Networks of Type-I and Type-II Excitable Systems

  • Eckehard SchöllEmail author
  • Judith Lehnert
  • Andrew Keane
  • Thomas Dahms
  • Philipp Hövel
Conference paper
Part of the Understanding Complex Systems book series (UCS)

Abstract

We discuss synchronization and desynchronization transitions in networks of delay-coupled excitable systems. These transitions arise in response to varying the balance of excitatory and inhibitory couplings in a small-world topology. To describe the local dynamics, we use generic models for type-I excitability, which arises close to a saddle-node bifurcation on an invariant cycle (SNIC or SNIPER), and for type-II excitability, which occurs close to a Hopf bifurcation (FitzHugh-Nagumo model). For large delay times both type-I and type-II systems behave in a similar way. This is different for small delay times, where in case of type-I excitability we find novel multiple transitions between synchronization and desynchronization, when the fraction of inhibitory links is increased. In contrast, only a single desynchronization transition occurs for the FitzHugh-Nagumo model (type-II excitability) for all values of the delay time.

Keywords

Complex networks Delayed coupling Synchronization Excitatory and inhibitory balancing Type-I and type-II excitability Small-world 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Eckehard Schöll
    • 1
    Email author
  • Judith Lehnert
    • 1
  • Andrew Keane
    • 1
  • Thomas Dahms
    • 1
  • Philipp Hövel
    • 1
    • 2
  1. 1.Institut Für Theoretische PhysikTechnische Universität BerlinBerlinGermany
  2. 2.Bernstein Center for Computational NeuroscienceHumboldt-Universität zu BerlinBerlinGermany

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