Alternating chimeras in networks of ephaptically coupled bursting neurons (1809.02442v1)

Abstract: In this article, we report the development of an emerging dynamical state, namely, the alternating chimera, in a network of identical neuronal systems induced by an external electromagnetic field. Owing to this interaction scenario, the nonlinear neuronal oscillators are coupled indirectly via electromagnetic induction with magnetic flux, through which neurons communicate in spite of the absent physical connections among them. The evolution of each neuron, here, is described by the three-dimensional Hindmarsh-Rose dynamics. We demonstrate that the presence of such non-locally and globally interacting external environments induce a stationary alternating chimera pattern in the ensemble of neurons, whereas in the local coupling limit the network exhibits transient chimera state whenever the local dynamics of the neurons is of chaotic square-wave bursting type. For periodic square-wave bursting of the neurons, similar qualitative phenomenon has been witnessed with the exception of the disappearance of cluster states for non-local and global interactions. Besides these observations, we advance our work while providing confirmation of the findings for neuronal ensembles exhibiting plateau bursting dynamics. These results may deliver better interpretations for different aspects of synchronization appearing in network of neurons through field coupling that also relaxes the prerequisite of synaptic connectivity for realizing chimera state in neuronal networks.