Logistic Gene Regulatory Networks: Prevention of Expression Shutdown, and Numerical Stability Beyond Hill Function

arXiv:2605.01056v1 Announce Type: new Abstract: Hill functions, the standard tool for modelling gene regulatory networks, carry three structural flaws when the cooperativity exponent is non-integer: loss of global smoothness, silent complex-valued arithmetic corruption of ODE trajectories, and an identically zero basal production rate that traps bistable models in off-states. Logistic functions $f^\pm$, being globally $C^\infty$, real-valued for all arguments, and strictly positive at zero, reso...