System Dynamics & Control Theory: Dynamic Systems Formulation of Persistence Science

Abstract

This paper develops a dynamic systems formulation of Persistence Science. Building upon The Odero Axiom, the Information Index, and the Persistence Index, the framework transforms the persistence condition into a continuous temporal state-space model governed by Persistence Capacity (P), the Persistence Index (Ω), Omega Velocity (ω), Omega Acceleration (α), and the expanded state vector Ψ(t). The framework develops the normalized Persistence Index (Ω = P/D), the central dynamic trajectory velocity equation, second-order acceleration dynamics, and the expanded temporal state vector. The theory establishes the calculus of Omega Velocity and Omega Acceleration, introduces the Persistence Control-Phase Simplex, formalizes a four-factor scalar decay decomposition, and derives optimization conditions for structural persistence under resource constraints. The framework further generates falsifiable predictions concerning collapse dynamics, phase-boundary hysteresis, and decay-channel dominance. System Dynamics & Control Theory provides the dynamic and state-space foundation of Persistence Science and extends the framework from static persistence conditions to continuous persistence trajectories.