Determine the effect of slow-to-fast feedback on synchronization-driven regimes

Determine whether the synchronization-driven regimes identified in the unidirectional, feedback-free fast–slow systems persist, are enhanced, or are suppressed when feedback from the slow response subsystem to the fast intermittent driver is reintroduced.

Background

The study deliberately considers a unidirectional configuration in which the fast subsystem forces the slow subsystem but receives no feedback. This setup isolates how intermittent forcing reshapes the response attractor, induces regime transitions, and produces phase locking.

The authors identify reintroducing feedback from the slow subsystem to the fast subsystem as a natural extension and leave unresolved whether the synchronization-mediated regimes found in the one-way configuration remain stable, become stronger, or disappear when the two subsystems interact bidirectionally.

References

A natural extension is to reintroduce feedback from the slow to the fast subsystem, and to assess whether the synchronization-driven regimes identified here persist, are enhanced, or are suppressed once the response is allowed to act back on its driver.

— Intermittency-induced transitions in fast-slow dynamical systems  (2609.25513 - Barone et al., 22 Sep 2026) in Section 5, subsection “Future perspectives”

Likewise, a natural direction for future work is to test whether the mechanisms identified here, namely the exponential delay scaling and the synchronization-driven regime transitions, extend to intermittent phenomena in systems of increasing complexity.

— Intermittency-induced transitions in fast-slow dynamical systems  (2609.25513 - Barone et al., 22 Sep 2026) in Section 5, subsection “Future perspectives”

We hypothesize that this band is, at least in part, associated with the onset of phase synchronization between the two subsystems: a strong coupling constrains the phase of $\mathbf{X}_2$ to follow that of the driver, thereby restricting the accessible region of phase space and compressing the tail of the extreme value distribution relative to the weakly coupled, fully chaotic regime (see Section \ref{SEC:RESP}).

— Intermittency-induced transitions in fast-slow dynamical systems  (2609.25513 - Barone et al., 22 Sep 2026) in Section 3, subsection “Extreme emergence”