Integrating Debt Dynamics and Planetary Boundaries Through a Catastrophe Theory Model of Financial Ecological Collapse

Abstract This paper develops a novel nonlinear dynamical system to analyze the interaction between financial instability and ecological overshoot. Using catastrophe theory and bifurcation analysis, I demonstrate how accelerating debt growth and environmental degradation create hysteresis loops, leading to irreversible economic collapse. This study introduces the first catastrophe theory framework unifying Minsky’s financial instability and planetary boundaries, identifying dual critical thresholds in debt/GDP ratios (ϕ>0.07) and carbon budgets (ϵ > 0.12) that trigger irreversible collapse.