Structural stability

The mathematical models we devise to make sense of the world around and within us can only be approximations. Therefore, it seems reasonable that if they are to accurately reflect reality, the models themselves must be somewhat insensitive to perturbations. The attempts to give mathematical substance to these rather vague ideas have led to the concept of structural stability.

The concept of structural stability was introduced by Andronov and Pontryagin (1931) and has played a central role in the development of dynamical systems theory. Roughly speaking, a dynamical system (vector field or map) is said to be structurally stable if nearby systems have qualitatively the same dynamics.