Bifurcation, Tipping, and Regime Shifts in Nonlinear Energy-Balance Models

Summary

This feature paper develops a potential-function framework for interpreting tipping points and regime shifts in nonlinear energy-balance models. It defines a tipping process as a coupled bifurcation and transition, then compares linear, quadratic, and cubic model forms. The quadratic model illustrates abrupt globally unstable tipping, while the cubic model exhibits bistability, hysteresis, and critical slowing down. The analysis clarifies how curvature, stability, forcing, and irreversible transitions can be interpreted within a common potential-landscape view.