Turbulence due to spiral breakup in a continuous excitable medium

Abstract

Excitable media are extended spatial systems, which support the propagation of waves including pulses and rotating spirals. They are well described by sets of partial differential equations involving a fast activator and a slow inhibitor variable. Here we show that spiral breakup, leading to turbulence, can occur in a two-dimensional reaction-diffusion system with delayed-inhibitor production. Upon a decrease of excitability, spirals become unstable because their wavelengths and periods are too short to be sustained in the system.