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

• 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
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2016-02661-4

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.