Abstract
We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities.
Highlights
Synchronization phenomena are widely studied across fields, from classical mechanics [1] to complex dynamical systems [2,3,4,5] and music [6, 7]
We focus on the possibility to observe chimera-like patterns in a multiplex structure of a realworld system, namely the neuronal network of Caenorhabditis elegans (C. elegans)
We introduce an alternative way of finding meaningful communities in the neuronal network and relate the observed synchronization patterns—including chimera-like states – to biological functions of the involved neurons
Summary
Synchronization phenomena are widely studied across fields, from classical mechanics [1] to complex dynamical systems [2,3,4,5] and music [6, 7]. This consensus was revised when chimeras were found in systems of globally [36,37,38,39,40,41] and locally coupled oscillators [42,43,44,45,46,47] These regular topologies often capture the nature of the interaction between the coupled elements, there are many real-world systems where a more complex connectivity description is required. Prominent examples of such systems are biological neuron networks, where synchronization is important for various cognitive functions, and chimera states, in particular, can be used to interpret phenomena such as epileptic seizures [48] and bump states [49, 50]
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