Exponential system-size dependence of the lifetime of transient spiral chaos in excitable and oscillatory media

TL;DR

This paper derives a general exponential expression for the lifetime of transient spiral chaos in excitable and oscillatory media, validated by numerical simulations, aiding predictions in large systems.

Contribution

It provides a novel analytical expression for the system size dependence of transient chaos lifetime, based on the Gaussian distribution of spiral counts.

Findings

Lifetime increases exponentially with system size.

The derived expression matches numerical results.

Applicable to both excitable and oscillatory media.

Abstract

Excitable media can develop spiral chaos, in which the number of spirals changes chaotically with time. Depending on parameter values in dynamical equations, spiral chaos may permanently persist or spontaneously arrive at a steady state after a transient time, referred to as the lifetime. Previous numerical studies have demonstrated that the lifetime of transient spiral chaos increases exponentially with system size to a good approximation. In this study, using the fact that the number of spirals obeys a Gaussian distribution, we provide a general expression for the system size dependence of the lifetime for large system sizes, which is indeed exponential. We confirm that the expression is in good agreement with numerically obtained lifetimes for both excitable and oscillatory media with parameter sets near the onset of transient chaos. The expression we develop for the lifetime is expected to be useful for predicting lifetimes in large systems.