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

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 L...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2016-09, Vol.225 (6-7), p.1149-1164
Main Authors: Tsigkri-DeSmedt, N.D., Hizanidis, J., Hövel, P., Provata, A.
Format: Article
Language:English
Subjects:
Atomic
Axons
Classical and Continuum Physics
Condensed Matter Physics
Coupling
Fractals
Materials Science
Mathematical Modeling of Complex Systems
Measurement Science and Instrumentation
Molecular
Network topologies
Nonlinear dynamics
Optical and Plasma Physics
Physics
Physics and Astronomy
Refractory period
Regular Article
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Summary: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.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjst/e2016-02661-4