Chimera-like States in Modular Neural Networks.

Johanne Hizanidis,Nikos E Kouvaris,Gorka Zamora-López,Albert Díaz-Guilera,Chris G Antonopoulos

doi:10.1038/srep19845

Abstract

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.

Highlights

One of the most challenging complex system is the human brain in which neurons and their interconnections through synapses form a very complicated structure, the cortical network
In this work we have quantified and compared certain measures of dynamical complexity, such as synchronization, which may underpin the “differentiation” in sub-domains and the “integration” as the system exhibits coherent behavior as a whole[56] and, the metastability λ and chimera-like χ indices that allow for the quantification of the degree of metastability and chimera-like behavior exhibited by the system and its communities
In10, various statistical quantities associated with the C. elegans neural network, such as the global clustering coefficient, the average of local clustering coefficients, the mean shortest path, the degree probability distribution function of the network and the small-worldness measure have been computed

Summary

Introduction

One of the most challenging complex system is the human brain in which neurons and their interconnections through synapses form a very complicated structure, the cortical network. It has been revealed that the cortical network is hierarchical and clustered with a complex connectivity[2], known as the modular organization of the brain This demands an inherent parallel nature of brain computations[3]. It was shown that its neural system has the ability to distinguish between tastes, odours or any indication related to the presence or absence of food It shows different kinds of learning behavior, including associative learning such as classical conditioning and differential classical conditioning, and non-associative forms of learning such as habituation and dishabituation[15]. These properties, though quite “simple”, are reminiscent of the human brain ability to adapt to different stimuli and environments. Insightful findings regarding synchronization in complex networks have been reviewed in ref. 17 and, recently, synchronization in complex modular or clustered networks has been investigated in ref

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