Parametric resilience in a closed ecological reactor: The Wood Wide Web as a distributed PID controller for life support

Closed bioregenerative life-support systems must maintain stability under fluctuating environmental conditions without heavy external control. We present a 3D reaction-diffusion-chemotaxis model of a toroidal reactor that couples plant physiology, water cycling, and a mechanistic mycorrhizal network known as the "Wood Wide Web". Homogeneous stability analysis reveals a bistable system with an unstable "Off" state and a productive "On" state activated by an initial mycorrhizal impulse. The bifurcation occurs exactly at cooperation coefficient γ = 0: for γ ≤ 0 the homogeneous state is marginally stable, while for γ > 0 the biological instability grows linearly. Under periodic forcing mimicking the day/night cycle, the Wood Wide Web sustains a stable forced limit cycle, demonstrated by stroboscopic Poincaré sections and return maps. When the model is re-dimensionnalised to separate the fast timescales of photosynthesis from the slow timescales of mycelial growth, a new and unexpected property emerges: parametric resilience . The steady-state CO ₂ concentration remains confined within a narrow band (less than 16% variation) despite a 2.5-fold change in the cooperation coefficient γ and a 42-fold change in the mycorrhizal signal speed. The critical cooperation threshold γ _crit beyond which the system departs from homeostasis follows a precise power law, γ _crit ∝speed ^− 0.86 (R ²  = 0.99), transforming the sharp bifurcation of the dimensionless model into a smooth, engineerable curve. We interpret this behaviour through the lens of control theory: the Wood Wide Web functions as a distributed PID controller, where the signal speed controls the effective time delay of the feedback loop. This framework provides a quantitative design rule for reliable, maintenance-free bioregenerative life support, in which biological cooperation replaces centralized control.