A robust Hopf-organized morphological boundary in initial-condition-dependent Gray–Scott phase diagrams

Morphological diagrams of the Gray–Scott model are constructed in the feed–kill plane for threeinitial conditions, using spatial, temporal, and geometric metrics. Although several regions dependon the initial perturbation, the boundary between the active homogeneous state and the temporallyvariable state is suggested to be invariant: when the three boundaries are compared, 94.91% of thepoints do not exceed two vertical grid steps. The mean separation from the lower Hopf branch was7.20 grid steps, indicating that the transition is organized by this instability.