We study the emergence of chimera states in a multilayer neuronal network,
where one layer is composed of coupled and the other layer of uncoupled
neurons. Through the multilayer structure, the layer with coupled neurons acts
as the medium by means of which neurons in the uncoupled layer share
information in spite of the absent physical connections among them. Neurons in
the coupled layer are connected with electrical synapses, while across the two
layers neurons are connected through chemical synapses. In both layers the
dynamics of each neuron is described by the Hindmarsh-Rose square wave bursting
dynamics. We show that the presence of two different types of connecting
synapses within and between the two layers, together with the multilayer
network structure, plays a key role in the emergence of between-layer
synchronous chimera states and patterns of synchronous clusters. In particular,
we find that these chimera states can emerge in the coupled layer regardless of
the range of electrical synapses. Even in all-to-all and nearest-neighbor
coupling within the coupled layer, we observe qualitatively identical
between-layer chimera states. Moreover, we show that the role of information
transmission delay between the two layers must not be neglected, and we obtain
precise parameter bounds at which chimera states can be observed. The expansion
of the chimera region and annihilation of cluster and fully coherent states in
the parameter plane for increasing values of inter-layer chemical synaptic time
delay are illustrated using effective range measurement. These results are
discussed in the light of neuronal evolution, where the coexistence of coherent
and incoherent dynamics during the developmental stage is particularly likely.Comment: 15 pages, 12 figure
