Synchronisation and Chimera States in Modular Networks of Coupled Neurons

Chimera states, namely the coexistence of coherent and incoherent behaviour, were previously analysed in complex networks. However, they have not been extensively studied in modular networks. In this talk Dr Kouvaris will present recently published results and discuss the current research on this topic.

In [1] a neural network inspired by the connectome of the C. elegans soil worm, organized into six interconnected communities, where neurons obey chaotic bursting dynamics was considered. Neurons are assumed to be connected with electrical synapses within their communities and with chemical synapses across them. As the numerical simulations reveal, the coaction of these two types of coupling can shape the dynamics in such a way that chimera-like states can happen. They consist of a fraction of synchronised neurons which belong to the larger communities, and a fraction of desynchronised neurons which are part of smaller communities. In addition to the classical order parameter ρ, other measures of coherence were also employed, such as the chimera-like χ and metastability λ indices, which quantify the degree of synchronisation among communities and along time, respectively.

A new approach to this structurally induced chimera states will also be discussed for prototype modular networks of coupled phase oscillators [2].

[1] Hizanidis, Kouvaris, Zamora-Lopez, Diaz-Guilera and Antonopoulos, Sci Rep. 6 19845 (2016)

[2] Zamora-Lopez, Kouvaris, Pereira and Deco (in preparation 2017)