Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback

TL;DR

This paper investigates how nonlocal spatial coupling and time-delayed feedback can control the onset of traveling pulses in reaction-diffusion systems, offering insights into brain pattern formation and pathological pulse control.

Contribution

It introduces a hybrid model combining reaction-diffusion dynamics with augmented transmission control, revealing how these mechanisms influence pulse propagation and excitability.

Findings

Traveling pulses are primarily solutions to the reaction-diffusion equations.

Augmented transmission modifies excitability, affecting pulse onset.

New patterns like step-wise propagation emerge outside moderate control settings.

Abstract

The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by augmented transmission capability that is provided either along nonlocal spatial coupling or by time-delayed feedback. We show that traveling pulses occur primarily as solutions to the RD equations while augmented transmission changes excitability. For certain ranges of the parameter settings, defined as weak susceptibility and moderate control, respectively, the hybrid model can be mapped to the original RD model. This results in an effective change of RD parameters controlled by augmented transmission. Outside moderate control parameter settings new patterns are obtained, for example step-wise propagation due to delay-induced oscillations. Augmented transmission constitutes a signaling system complementary to the classical RD mechanism of pattern formation. Our hybrid model combines the two major signaling systems in the brain, namely volume transmission and synaptic transmission. Our results provide insights into the spread and control of pathological pulses in the brain.