Structural Stability
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In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by continuously differentiable|C1-small perturbations.Examples of such qualitative properties are numbers of fixed point (mathematics)|fixed points and periodic orbits (but not their periods). Unlike Lyapunov stability, which considers perturbations of initial conditions for a fixed system, structural stability deals with perturbations of the system itself. Variants of this notion apply to systems of ordinary differential equations, vector fields on smooth manifolds and flow (mathematics)|flows generated by them, and diffeomorphisms. Structurally stable systems were introduced by Aleksandr Andronov and Lev Pontryagin in 1937 under the name systèmes grossières, or rough systems. They announced a characterization of rough systems in the plane, the Andronov–Pontryagin criterion. In this case, structurally stable systems are typ...
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