Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

TL;DR

This paper explores how different types of time-delayed coupling influence spatiotemporal coherence and synchronization in small-world neuronal networks of noisy Terman-Wang neurons, revealing resonance phenomena and various synchronized states.

Contribution

It demonstrates the distinct effects of two types of time-delayed coupling on neuronal network dynamics, including resonance-induced order and transitions to complex synchronized states.

Findings

Time delay enhances coherence and synchronization when matched to intrinsic spike period.

Different coupling types lead to distinct synchronization phenomena, including chimera states.

Noise intensity and network rewiring influence the observed dynamical behaviors.

Abstract

We investigate temporal coherence and spatial synchronization on small-world networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence on two types of time-delayed coupling: $\{x_j(t-\tau)-x_i (t)\}$ and $\{x_j(t-\tau)-x_i(t-\tau)\}$. For the former case, we show that time delay in the coupling can dramatically enhance temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time $\tau$ is tuned to nearly match the intrinsic spike period of the neuronal network, the system dynamics reaches a most ordered state, which is both periodic in time and nearly synchronized in space, demonstrating an interesting resonance phenomenon with delay. For the latter case, however, we can not achieve a similar spatiotemporal ordered state, but the neuronal dynamics exhibits interesting synchronization transition with time delay from zigzag fronts of excitations to dynamic clustering anti-phase synchronization (APS), and further to clustered chimera states which have spatially distributed anti-phase coherence separated by incoherence. Furthermore, we also show how these findings are influenced by the change of the noise intensity and the rewiring probability. Finally, qualitative analysis is given to illustrate the numerical results.