Ghost Dynamics in Receptor Signalling Networks: A Fast--Slow Adaptive Extension of Competitive Cancer Inhibition Models

What the math gives to ML

The paper provides a transferable fast–slow mechanism: a rapidly relaxing variable can be reduced quasi-steadily, while a slowly adapting variable can move an activity subsystem through a saddle-node fold. Near the fold, trajectories exhibit a quantitatively predictable ghost delay, with residence time proportional to the inverse square root of the distance from the fold and, under slow transverse passage, a delay of order \(\varepsilon^{-1/3}\). This suggests neural architectures with fast feature states, slower adaptive context states, and an explicit fold-distance controller that allocates computation or memory when the network enters a ghost regime. The mechanism is especially promising for recurrent, state-space, neural-ODE, and long-horizon models because it predicts when transient persistence and delayed regime switching should occur rather than treating them as unexplained memory.