Structural stability

Summary

A dynamical system is structurally stable if every small enough perturbation of it has the same qualitative behaviour. More precisely, the phase portrait of the perturbed system is the image of the original one under a homeomorphism that maps trajectories to trajectories. Structural stability is about the stability of the whole system under changes of the equations, not of one solution under changes of the initial state. Models of the real world are only known approximately, so structurally stable models are the ones whose qualitative predictions can be trusted. See the definition.