Mechanism of bubble initiation in Lorenz networks

Determine whether, in networks of diffusively coupled chaotic Lorenz oscillators, the observed difference in the finite-time Lyapunov averaging-window behavior arises because bubbles are initiated when trajectories visit a neighborhood of the unstable steady state embedded in the synchronization manifold.

Background

Extending the finite-time transverse Lyapunov analysis from Rössler to Lorenz networks reveals a distinct behavior for the window size that maximizes amplification. The authors hypothesize that this difference stems from a different bubbling mechanism in Lorenz systems, specifically involving proximity to an unstable equilibrium on the synchronization manifold.

Verifying this mechanism would clarify how oscillator-specific invariant sets shape bubbling and the corresponding thresholds.

References

We conjecture that this difference is due to a bubble being initiated when the Lorentz trajectories visit a neighborhood of an unstable steady state (with zero period) embedded in the synchronization manifold.

— Bubbling in Oscillator Networks (2504.07374 - Tirabassi et al., 10 Apr 2025) in Results, Criterion #5: Finite-time transverse Lyapunov exponents (Lorenz generalization)