Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance

TL;DR

This paper investigates how long-range chemical-mediated coupling influences bursting synchronization in neural networks, revealing a transition from local to global coupling and exploring control methods for pathological neural rhythms.

Contribution

It introduces a one-dimensional model with exponential decay coupling, analyzing synchronization transitions and external signal effects in neural networks.

Findings

Synchronization transition occurs at a critical coupling value.

External periodic signals can modulate bursting synchronization.

Model allows continuous transition from local to global coupling.

Abstract

Many networks of physical and biological interest are characterized by a long-range coupling mediated by a chemical which diffuses through a medium in which oscillators are embedded. We considered a one-dimensional model for this effect for which the diffusion is fast enough so as to be implemented through a coupling whose intensity decays exponentially with the lattice distance. In particular, we analyzed the bursting synchronization of neurons described by two timescales (spiking and bursting activity), and coupled through such a long-range interaction network. One of the advantages of the model is that one can pass from a local (Laplacian) type of coupling to a global (all-to-all) one by varying a single parameter in the interaction term. We characterized bursting synchronization using an order parameter which undergoes a transition as the coupling parameters are changed through a critical value. We also investigated the role of an external time-periodic signal on the bursting synchronization properties of the network. We show potential applications in the control of pathological rhythms in biological neural networks.