Chimera states, namely the coexistence of coherent and incoherent behavior, were previously analyzed in complex networks. However, they have not been extensively studied in modular networks. Here, we consider a neural network inspired by the connectome of the C. elegans soil worm, organized into six interconnected communities, where neurons obey chaotic bursting dynamics. Neurons are assumed to be connected with electrical synapses within their communities and with chemical synapses across them. As our 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 synchronized neurons which belong to the larger communities, and a fraction of desynchronized neurons which are part of smaller communities. In addition to the Kuramoto order parameter ρ, we also employ other measures of coherence, such as the chimera-like χ and metastability λ indices, which quantify the degree of synchronization among communities and along time, respectively. We perform the same analysis for networks that share common features with the C. elegans neural network. Similar results suggest that under certain assumptions, chimera-like states are prominent phenomena in modular networks, and might provide insight for the behavior of more complex modular networks.

This study was supported by the J. S. Latsis Public Benefit Foundation in Greece. J. H. acknowledges support/nby the EU/FP7-REGPOT-2012 –2013-1 under grant agreement n316165. N. E. K. and A. D. -G. acknowledge/nsupport by the LASAGNE (Contract No. 318132) and MULTIPLEX (Contract No. 317532) EU projects as well/nas by the Generalitat de Catalunya (2014SGR608) and Spanish MINECO (FIS2012-38266). G. Z. -L. received/nsupport from the European Union Seventh Framework Programme FP7/2007–2013 under grant agreement/nnumber PIEF-GA-2012-331800.