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The European Physical Journal Special Topics

, Volume 225, Issue 6–7, pp 1149–1164 | Cite as

Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity

  • N.D. Tsigkri-DeSmedt
  • J. Hizanidis
  • P. Hövel
  • A. ProvataEmail author
Regular Article Session B: Papers I
Part of the following topical collections:
  1. Mathematical Modeling of Complex Systems

Abstract

The effects of nonlocal and fractal connectivity are investigated in a network of Leaky Integrate-and-Fire (LIF) elements. The idea of fractal coupling originates from the hierarchical topology of networks formed by neuronal axons, which transmit the electrical signals in the brain. If a number of LIF elements with finite refractory period are nonlocally coupled, multi-chimera states emerge whose multiplicity depends both on the coupling strength and on the refractory period. We provide evidence that the introduction of a hierarchical topology in the coupling induces novel complex spatial and temporal structures, such as nested chimera states and transitions between multi-chimera states with different multiplicities. These results demonstrate new complex patterns, as well as transitions between different multi-chimera states arising from the combination of nonlinear dynamics with the hierarchical coupling.

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Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  • N.D. Tsigkri-DeSmedt
    • 1
    • 2
  • J. Hizanidis
    • 1
    • 3
  • P. Hövel
    • 4
    • 5
  • A. Provata
    • 1
    Email author
  1. 1.Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”AthensGreece
  2. 2.Department of Solid State PhysicsDepartment of Physics, University of AthensAthensGreece
  3. 3.Crete Center for Quantum Complexity and Nanotechnology, Department of Physics, University of CreteHeraklionGreece
  4. 4.Institut für Theoretische Physik, Technische Universität BerlinBerlinGermany
  5. 5.Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu BerlinBerlinGermany

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