Map transversely unstable regions and residence times on the synchronization manifold

Identify and characterize the regions of the synchronization manifold of a diffusively coupled network of chaotic Rössler oscillators that have positive transverse local Lyapunov exponents, and determine how long typical trajectories reside in those regions (i.e., the residence-time statistics), in order to quantify the mechanisms that trigger bubbling events.

Background

The development of bubbles depends on how long trajectories remain in transversely unstable parts of the synchronization manifold. While local transverse Lyapunov exponents (LLEs) vary strongly along the attractor, directly identifying the unstable regions and quantifying residence times are crucial to understanding and predicting bubble initiation.

The authors use finite-time transverse Lyapunov exponents and visualizations to gain insight, but explicitly note that the precise locations of positive-LLE regions and their residence times are not known.