2026/02/21 by Bernd von Mallinckrodt · 1 voice
#Bifurcation #Control theory (sociology) #Dissipative system #Dynamical systems theory #Fragility #Nonlinear system #Robustness (evolution) #Scaling #Stability (learning theory)
paper · doi:10.5281/zenodo.18722917
published in Open MIND
openalex publication_date 2026/02/21 · openalex created_date 2026/02/22 · openalex updated_date 2026/07/15
This work presents a minimal diagnostic framework for assessing structural stability and stochastic fragility in coupled dissipative systems with asymmetric constraint–performance feedback. The model integrates deterministic bifurcation structure, non-normal linear reactivity, basin geometry, and stochastic escape dynamics into a compact two-dimensional representation. The system couples a nonlinear resonance variable with a secondary constraint variable. A dimensionless robustness ratio κ characterizes deterministic stability. In addition to classical eigenvalue analysis, the framework incorporates numerical abscissa, transient amplification, basin erosion, and Kramers-type escape scaling to evaluate effective resilience under stochastic forcing. The central contribution is not a universal theory of complex systems, but a reduced-order diagnostic structure that connects: • deterministic fixed-point stability • non-normal transient growth • phase-space separatrix deformation • quasi-potential barrier scaling • mean time to collapse (MTTC) estimation The framework provides a compact stability assessment toolkit applicable to reduced-order representations of technical, physical, and resource-constrained performance systems exhibiting asymmetric feedback. Scope limitations are explicitly acknowledged: the model is two-dimensional, equilibrium-dependent, and intended as a structural prototype rather than a complete high-dimensional theory. Nonlinear Dynamics; Dissipative Systems; Non-Normality; Stochastic Escape; Basin of Attraction; Stability Diagnostics; Robustness Ratio; Transient Growth