2026/03/19 by Bernd von Mallinckrodt · 1 voice
Computer Science · Environmental Science · Physics and Astronomy · #Chaos, Complexity, and Education #Complex Systems and Dynamics #Ecosystem dynamics and resilience
paper · doi:10.5281/zenodo.19108084
openalex publication_date 2026/03/19 · openalex created_date 2026/03/20 · openalex updated_date 2026/07/01
This paper introduces a minimal two-variable dynamical system coupling adaptive capacity R(t) and structural rigidity Φ(t) in complex adaptive systems. The model is motivated by Holling’s rigidity trap hypothesis, Scheffer’s critical transitions framework, and March’s exploration-exploitation trade-off. Two dimensionless coupling parameters (λ, μ) govern the qualitative behaviour of the system. In the bistable regime, the interior equilibrium is a saddle point whose stable manifold separates trajectories leading to a resilience-dominant state from those converging to a low-adaptive-capacity collapse state. The bifurcation boundary λμ = αγ is derived analytically. Near this boundary, the model predicts critical slowing down consistent with empirical early-warning signals documented in ecological and social systems. Ecological variance metrics and firm-level efficiency ratios are proposed as observable proxies. The contribution is intentionally minimal: a tractable two-parameter structure for generating falsifiable predictions about collapse onset, positioned as a formal complement to existing resilience and critical transitions theory. adaptive capacity · structural rigidity · complex adaptive systems · critical transitions · bistability · resilience · collapse dynamics · tipping points · saddle-node bifurcation · early warning signals · panarchy · rigidity trap · exploration exploitation · nonlinear dynamics · dynamical systems · phase portrait · regime shifts · systems theory · complexity science · theoretical biology