Geometric Singular Perturbation Theory

GSPT has become the mathematical foundation for understanding timescale separation in complex systems. It justifies the practice of adiabatic elimination, explains the conditions under which hierarchical models are valid, and identifies the mechanisms — canard explosions, fold bifurcations, and relaxation oscillations — by which the separation of timescales breaks down. In this sense, GSPT is not a specialized technique but a general theory of how hierarchical levels emerge from dynamical structure.