Category: Nonlinear Dyn.

Summary: Testing whether adaptive delayed control in the Gray-Scott model has an optimal delay window whose benefit depends on diffusion anisotropy.

Reaction-diffusion systems can often be steered by feedback, but delayed control does not usually help uniformly across all parameter settings. This experiment asks whether the Gray-Scott model has a beneficial delay window for adaptive feed-rate control, and whether that window changes once diffusion becomes anisotropic rather than directionally uniform.

The simulation runs many GPU-accelerated trials over combinations of feedback delay and anisotropy, then summarizes how much adaptive control improves the targeted pattern metric. It also records whether the gain is strongest at intermediate delays and whether highly anisotropic conditions amplify or suppress the benefit.

The scientific point is to treat delay and anisotropy as interacting controls rather than independent tweaks. That helps identify whether feedback timing can compensate for directional transport biases in nonlinear pattern-forming media.

Method: GPU-accelerated Gray-Scott simulations sweeping delayed adaptive feedback settings and diffusion anisotropy, aggregated over repeated trials.

What is measured: Adaptive gain, mid-delay gain, high-anisotropy gain, best delay, positive-pair fraction, and trial-to-trial variability.