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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Kaori Sugimura, Hiroshi Kori

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.

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Citations

Sep 28, 2017·Physical Review Letters·Thomas LilienkampUlrich Parlitz
Mar 17, 2018·Physical Review Letters·Thomas Lilienkamp, Ulrich Parlitz
Feb 17, 2018·Physical Review. E·G GambinoM Sammartino
Oct 24, 2018·Biophysics and Physicobiology·Hiroyuki Kitahata, Masanobu Tanaka

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