Time delayed chemical synapses and synchronization in multilayer neuronal networks with ephaptic inter-layer coupling

Abstract

In this paper, a three-layer neuronal network is studied to consider different complex connections between the neurons. In the nervous system, the communication between the neurons is mostly based on the electrical and chemical synapses. However, extracellular electric fields can induce a magnetic flux which can lead to indirect neural communications, by means of electromagnetic induction. This mode of coupling is called ephaptic coupling, which here is used between the layer. To describe the coupling within the layers, the electrical and chemical synapses are defined. We also take into account the partial time delays, to reflect the required time for information transmission through chemical synapses. Particularly, we consider partial and full time delays, as well as strong and weak coupling strengths. It is shown that three layers typically have opposite synchronization properties in the strong and weak coupling regimes. Specifically, when the coupling is strong, the top and bottom layers are synchronous, while the middle layer is desynchronous. But when the coupling is weak, the middle layer is synchronous, while the top and bottom layers are desynchronous. In overall, the most synchrony is obtained when the weak coupling is accompanied with partial time delays in chemical communications. Our research sheds new light on the complex interplay between the time delay, the ephaptic coupling, and the synchronization in neuronal networks.