Toward a General Theory of Regulated Stability: A Formal Architectural Framework with Application to Wildfire Ecology

AbstractMany cross-disciplinary theories of stability invoke universal scalar invariants —constants presumed to hold across domains and scales. This paper argues that suchclaims conflate two distinct properties: structural invariance, the preservation ofbounded system behaviour under perturbation, and scalar universality, the emergence ofdomain-independent numerical constants. This conflation has impeded the developmentof a rigorous, domain-agnostic account of how open systems maintain regulatedstability.This paper introduces a formal framework — the General Theory of Regulated Stability(GTRS) — grounded in a Lyapunov-like functional ensuring bounded divergence underconstraint-preserving dynamics. The framework distinguishes intrinsic drift fromregulatory constraint feedback and defines homeostasis as a structural property ofdynamical systems rather than a scalar invariant. Critically, the framework applies toopen systems where regulatory feedback sustains bounded structure, in contrast toclosed systems where unconstrained entropy accumulation drives degradation.The framework is instantiated through Australian wildfire ecology, where fuelaccumulation, moisture regimes, biodiversity buffering, and landscape heterogeneityconstitute a naturally observable regulated system. The analysis demonstrates howconstraint feedback maintains bounded oscillatory fire regimes, and how degradation ofconstraint feedback shifts the system toward regimes characterised by increasedsusceptibility to large-scale fire events.No claims of universal constants or critical exponents are made. The contribution isarchitectural: a formal foundation for regulated stability applicable across ecological,neural, and engineered systems.