Category: Nonlinear Dyn.

Summary: Evaluating whether adaptive feedback in a noisy bistable Schlogl-like system is most effective at an intermediate observation delay, producing a delay-resonance window in switching coherence.

Bistable systems can switch between alternative states under noise, and feedback control may either regularize those switches or interfere with them depending on timing. This experiment asks whether adaptive gain control in a Schlogl-like bistable process has a resonant delay window where switching becomes more coherent than under fixed-gain control.

The script simulates a one-dimensional two-well dynamics with Ornstein-Uhlenbeck colored noise, delayed observations, and feedback that adapts its gain to recent variance. For each delay it compares fixed and adaptive control, then measures switching coherence and a resonance index that captures whether the adaptive advantage peaks away from the zero-delay and long-delay edges.

That focus makes the project a timing question rather than a generic control benchmark. The aim is to identify whether adaptive feedback and observation delay interact non-monotonically, creating a middle-delay regime where control works unusually well before degrading again.

Method: Repeated simulations of a Schlogl-like bistable system with colored noise, delayed feedback, and adaptive gain updates, summarized by switching-coherence and resonance metrics across delay values.

What is measured: Switching coherence under fixed and adaptive control, delay of peak adaptive advantage, resonance index, trial-level peak-delay estimates, and trial-level resonance strengths.