Astero Provata (National Center for Scientific Research Demokritos, Athens)

Title: The influence of the network connectivity in the spatial patterns of chimera states

Abstract: Chimera states emerge in systems of nonlocally coupled identical oscillators and are characterized by the coexistence of alternating coherent and incoherent domains. These hybrid states appear unexpectedly since all elementary oscillators in the network are identical and are identically coupled. A characteristic feature of chimera states is their mean frequency profile: In the coherent regions, all elements have equal, constant mean phase velocity, while in the incoherent ones the frequency profiles take arc shapes.  Here we present synchronization properties leading to chimera states in networks of coupled neuronal oscillators. To understand the influence of connectivity in the chimera form we investigate the Leaky Integrate and Fire (LIF) model under different connectivity architectures. In the case of nonlocal connectivity, we show evidence of a coexistence state where multileveled chimera patterns are formed and they coexist with domains consisting of near-threshold elements. The oscillating elements form complex mean phase velocity profiles while the potentials of the near-threshold elements present small fluctuations and never drop to the resting state. We study different synchronization patterns in the parameter space of the LIF system when the oscillators are nonlocally coupled in 1, 2 and 3 spatial dimensions. We also investigate the effects of different connectivity schemes: nonlocal connectivity, reflecting coupling, diagonal or hierarchical (fractal) connectivity.

– Tsigkri-DeSmedt, N.D., Hizanidis, J., Schöll, E., Hövel, P., Provata, A.
Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities,
European Physical Journal B 90(7),139 (2017).

– Tsigkri-DeSmedt, N.D., Hizanidis, J., Hövel, P., Provata, A.
Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity,
European Physical Journal: Special Topics 225(6-7), pp. 1149-1164 (2016).

– Schmidt, A., Kasimatis, T., Hizanidis, J., Provata, A., Hövel, P.
Chimera patterns in two-dimensional networks of coupled neurons
Physical Review E 95(3),032224 (2017).