A Minimal Dynamical Mechanism for Memory-Driven Resilience in Adaptive Systems

This paper introduces the Triadic Staircase, a minimal dynamical mechanism for the emergence of resilience in adaptive systems. The model consists of cyclic interaction among three modes — Potential State (L), Propagating State (P), and Stabilised State (B) — coupled to a Memory Accumulator (M) that records non-canceling deviations. Analytical results show that the local contraction rate toward equilibrium increases monotonically with accumulated memory. Numerical simulations confirm a corresponding decrease in recovery time following perturbations, and a Lyapunov verification confirms exact agreement between theoretical and simulated decay to floating-point precision. The work isolates a general principle: resilience can emerge endogenously through the accumulation of history, without requiring fine-tuned initial conditions or external control. This paper provides the first minimal dynamical instantiation of the triadic temporal framework introduced in the companion works (Jelenic 2026, DOI: 10.5281/zenodo.19626338 and 10.5281/zenodo.19646547).