Eur. Phys. J. B 60, 507-513 (2007)
https://doi.org/10.1140/epjb/e2008-00009-1

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

¹ China Academy of Engineering Physics, Mianyang, Sichuan, 621000, P.R. China
² Department of Physics, Peking University, Beijing, 100871, P.R. China
³ Department of Mathematics, North University of China, Taiyuan, Shan'xi, 030051, P.R. China
⁴ Department of Physics, Northeastern University, Boston, MA, 02115, USA

Corresponding author: ^a liuqx315@sina.com

Received: 1 August 2007
Revised: 1 October 2007
Published online: 16 January 2008

Abstract

It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. 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, reversal phenomena are observed in this system based on the numerical experiments in the one-dimensional space. We explain this as an effect of periodic forces. Thus, we give qualitative explanations for how stable reversal phenomena appear, which seem to arise from the mixing function of the periodic force and the noise. The output period and three velocities (normal, positive and 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.