Dynamics of Coupled Oscillator Systems - Abstract

Lilienkamp, Thomas

Features of transient chaos in coupled oscillators and extended systems

Many (high dimensional) dynamical systems, including networks of oscillators and excitable media, exhibit chaotic dynamics which is not persistent but transient. For extended systems the length of the transient typically grows exponentially with the system size (supertransients) and for a large class of systems 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 [1,2]. 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 and U. Parlitz, Phys. Rev. Lett. 120, 094101 (2018) [2] T. Lilienkamp and U. Parlitz, Phys. Rev. E 98, 022215 (2018)