Dynamic hysteresis in an autocatalytic reaction network

What the math gives to ML

The paper provides a constructive mechanism for dynamic hysteresis: a periodically driven bistable birth-death system develops a delayed response when the drive timescale is comparable to the intrinsic relaxation time. Its transferable asset is a nonlinear latent state with two metastable attractors, together with a measurable hysteresis-loop area that vanishes for quasistatic and excessively rapid forcing and peaks at an intermediate frequency. This can be implemented as a stochastic recurrent or state-space cell, where input-dependent control modulates an autocatalytic latent variable. The predicted frequency and noise dependence gives a falsifiable diagnostic for whether the cell has acquired useful long-timescale memory rather than merely increased its parameter count.