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

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Selforganization in Complex Systems: The Past, Present, and Future of Synergetics

Part of the book series: Understanding Complex Systems ((UCS))

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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.

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Authors and Affiliations

  1. Institut Für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623, Berlin, Germany

    Eckehard Schöll, Judith Lehnert, Andrew Keane, Thomas Dahms & Philipp Hövel

  2. Bernstein Center for Computational Neuroscience, Humboldt-Universität zu Berlin, Philippstraße 13, 10115, Berlin, Germany

    Philipp Hövel

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  1. Eckehard Schöll
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  2. Judith Lehnert
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  3. Andrew Keane
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  4. Thomas Dahms
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  5. Philipp Hövel
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Correspondence to Eckehard Schöll .

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Editors and Affiliations

  1. Institut für Theoret. Physik I, Universität Stuttgart Institut für Theoret. Physik I, Stuttgart, Germany

    Günter Wunner

  2. Fachbereich Physik, Forschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Axel Pelster

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Schöll, E., Lehnert, J., Keane, A., Dahms, T., Hövel, P. (2016). Control of Desynchronization Transitions in Delay-Coupled Networks of Type-I and Type-II Excitable Systems. In: Wunner, G., Pelster, A. (eds) Selforganization in Complex Systems: The Past, Present, and Future of Synergetics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-27635-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-27635-9_3

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