Cardiac arrhythmias like ventricular fibrillation are governed by chaotic spatio-temporal dynamics in the heart muscle resulting in unstable spiral or scroll waves. However, in cardiac tissue and many other excitable media, this chaotic dynamics is often not persistent but transient and can be characterized by the length of the transient phase, which typically grows quickly with the system size (supertransients). Using extensive simulations employing different mathematical models of cardiac dynamics (e.g. Fenton-Karma model) we identify specific type-II supertransients by an exponential increase of transient lifetimes with the system size in 2D and present a detailed investigation of the dynamics (number and lifetime of spiral waves, Kaplan-Yorke dimension). In 3D, simulations exhibit an increase of transient lifetimes and filament lengths only above a critical thickness [1]. For all systems investigated the chaotic phase terminates abruptly, without any obvious precursors in commonly used observables. By probing the state space using perturbed trajectories we show the existence of a “terminal transient phase,” which occurs prior to the abrupt collapse of chaotic dynamics [2]. During this phase the impact of perturbations is significantly different from the earlier transient and particular patterns of (non)susceptible regions in state space occur close to the chaotic trajectories. We therefore hypothesize that even without perturbations proper precursors for the collapse of chaotic transients exist, which might be highly relevant for coping with spatiotemporal chaos in cardiac arrhythmias or brain functionality, for example.
[1] T.Lilienkamp, J. Christoph and U. Parlitz, Phys. Rev. Lett. 119, 054101 (2017) [2] T.Lilienkamp and U. Parlitz, Phys. Rev. Lett. 120, 094101 (2018)