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Sci Rep. 2016 Dec 13;6:39033. doi: 10.1038/srep39033.

Chimera states in uncoupled neurons induced by a multilayer structure.

Author information

1
Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India.
2
Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia.
3
CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia.

Abstract

Spatial coexistence of coherent and incoherent dynamics in network of coupled oscillators is called a chimera state. We study such chimera states in a network of neurons without any direct interactions but connected through another medium of neurons, forming a multilayer structure. The upper layer is thus made up of uncoupled neurons and the lower layer plays the role of a medium through which the neurons in the upper layer share information among each other. Hindmarsh-Rose neurons with square wave bursting dynamics are considered as nodes in both layers. In addition, we also discuss the existence of chimera states in presence of inter layer heterogeneity. The neurons in the bottom layer are globally connected through electrical synapses, while across the two layers chemical synapses are formed. According to our research, the competing effects of these two types of synapses can lead to chimera states in the upper layer of uncoupled neurons. Remarkably, we find a density-dependent threshold for the emergence of chimera states in uncoupled neurons, similar to the quorum sensing transition to a synchronized state. Finally, we examine the impact of both homogeneous and heterogeneous inter-layer information transmission delays on the observed chimera states over a wide parameter space.

PMID:
27958355
PMCID:
PMC5153648
DOI:
10.1038/srep39033
[Indexed for MEDLINE]
Free PMC Article

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