Eur. Phys. J. B (2017) 90: 139
https://doi.org/10.1140/epjb/e2017-80162-0

Regular Article

Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities

¹ Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”, 15310 Athens, Greece
² Section of Solid State Physics, Department of Physics, National and Kapodistrian University of Athens, Athens, Greece
³ Crete Center for Quantum Complexity and Nanotechnology, Department of Physics, University of Crete, 71003 Heraklion, Greece
⁴ Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
⁵ Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany

^a e-mail: a.provata@inn.demokritos.gr

Received: 18 March 2017
Received in final form: 22 May 2017
Published online: 24 July 2017

Abstract

The effects of attracting-nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which model the exchange of electrical signals between neurons. Earlier investigations have demonstrated that repulsive-nonlocal and hierarchical network connectivity can induce complex synchronization patterns and chimera states in systems of coupled oscillators. In the LIF system we show that if the elements are nonlocally linked with positive diffusive coupling on a ring network, the system splits into a number of alternating domains. Half of these domains contain elements whose potential stays near the threshold and they are interrupted by active domains where the elements perform regular LIF oscillations. The active domains travel along the ring with constant velocity, depending on the system parameters. When we introduce reflecting coupling in LIF networks unexpected complex spatio-temporal structures arise. For relatively extensive ranges of parameter values, the system splits into two coexisting domains: one where all elements stay near the threshold and one where incoherent states develop, characterized by multi-leveled mean phase velocity profiles.