Explain the plateau structure in Kuramoto–Sivashinsky response delays

Determine whether the plateau structure observed in the optimal response lag of the coupled Kuramoto–Sivashinsky system is a devil’s-staircase-like signature of deterministic synchronization.

Background

The response-delay analysis finds that the optimal lag in the coupled Kuramoto–Sivashinsky system becomes constant across neighboring values of the time-scale separation, producing successive plateaus before saturation.

The authors interpret this behavior as potentially characteristic of deterministic systems and reminiscent of a devil’s staircase, but the interpretation is not established.

References

We believe this plateau behavior is a signature typically associated with the response of purely deterministic systems, reminiscent of a devil's staircase \citep{jensen_complete_1983, pikovsky_synchronization_2001}.

— Intermittency-induced transitions in fast-slow dynamical systems  (2609.25513 - Barone et al., 22 Sep 2026) in Section 4, subsection “Delay response scaling and phase locking”