Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing

TL;DR

This study investigates how noise and periodic forcing influence traveling wave propagation, reversal phenomena, and wave velocities in a simplified Oregonator model of sub-excitable systems, revealing diverse wave behaviors and their underlying mechanisms.

Contribution

It provides new insights into wave dynamics under noise and periodic forcing, including wave reversal phenomena and velocity relationships, using a simplified model.

Findings

Different wave types depend on noise and periodic forces.

Reversal phenomena are caused by the interaction of noise and periodic forcing.

Wave velocities are related to the periodic forces and wave types.

Abstract

It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling waves under different noises and periodic forces, using a simplified Oregonator model. Depending on different noises and periodic forces, we have observed different types of wave propagation (or their disappearance). Moreover, the reversal phenomena are observed in this system based on the numerical experiments in the one-dimensional space. As an explanation, we regard it as the effect of periodic forces. Thus, we give qualitative explanations to how reversal phenomena stably appear, which seem to arise from the mixing function of the periodic force and the noise. And the output period and three velocities (the normal, the positive and the negative) of the travelling waves are defined and their relationship with the periodic forces, along with the types of waves, are also studied in sub-excitable system under a fixed noise intensity.