CRTI: Simulation-Based Proof of Concept for the Compression–Resonance–Tension Index in Complex Adaptive Systems

This preprint presents a simulation-based proof of concept for the Compression–Resonance–Tension Index (CRTI), a minimal dynamical framework proposed to diagnose structural fragility in complex adaptive systems. The CRTI model links three state variables — structural compression (C), adaptive resonance (Res), and systemic tension (T = C/Res) — through a coupled nonlinear ODE system. Numerical simulations demonstrate three qualitatively distinct dynamical regimes: stable equilibria, near-threshold dynamics, and resonance collapse. A bifurcation analysis identifies a sharp nonlinear transition at γ/ρ = 1, arising endogenously from the fixed-point structure of the resonance equation rather than from an externally imposed parameter. The reduced resonance equation belongs structurally to the class of fold bifurcation models used in resilience theory, and the slow–fast decomposition of the full system corresponds to established tipping-point formulations. A sensitivity analysis confirms that the bifurcation threshold is robust to ±20% parameter variation, with the critical ratio γ/ρ remaining within ±15% of unity across all tested perturbations. The model is intentionally minimal and empirically uncalibrated. Its purpose is to demonstrate that the proposed compression–resonance interaction generates mathematically tractable, collapse-like dynamics consistent with regime-shift behavior observed in ecological, organizational, and socio-technical systems. All simulation code is provided as supplementary material to ensure full computational reproducibility. This preprint has not undergone peer review. complex adaptive systemsnonlinear dynamicsbifurcation analysisresilience theorystructural fragilityregime shiftstipping pointsearly warning signalssystemic riskcollapse dynamicscompression-resonance-tension indexCRTIfold bifurcationLotka-Volterracomplexity science