2026/02/15 by Bernd von Mallinckrodt · 1 voice
paper · doi:10.5281/zenodo.18652158
openalex publication_date 2026/02/15 · openalex created_date 2026/02/16 · openalex updated_date 2026/07/01
This preprint introduces a minimal nonlinear dynamical model formalizing structural over-constraint in adaptive organizations and complex systems. The framework translates qualitative systems-theoretical diagnoses of rigidity and resilience loss into a three-dimensional ordinary differential equation model governing structural permeability (P), constraint intensity (N), and effective variance (V). A reserve parameter (κ) captures buffering capacity and introduces a stabilizing feedback from variance to permeability. Local stability analysis reveals the existence of Hopf and fold bifurcations, as well as codimension-2 organizing structures. Global phase space geometry demonstrates basin shrinkage and separatrix crossing as the mechanism underlying abrupt regime transitions from adaptive oscillatory behavior to structurally singularized fixed-point states. Under stochastic perturbations of environmental uncertainty, collapse follows a noise-activated escape process consistent with large deviation theory. The mean time-to-collapse scales exponentially with the reserve parameter κ, formally linking structural redundancy and resilience. This work provides a formal bridge between systems theory, resilience research, and nonlinear regime transition analysis. The model is intentionally minimal and domain-agnostic; empirical calibration and numerical continuation analysis are designated as future extensions. Version 1.1 includes: • Structured model formulation • Stability and bifurcation analysis • Schematic basin geometry illustrations • Selected foundational references This document constitutes a preprint version intended for scholarly discussion and journal submission.