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A family of properties describing how trajectories near an invariant state or set behave under small perturbations. Lyapunov, asymptotic, orbital, and structural stability are distinct notions.
wp-math-stability-theorymit-ocw-nonlinear-dynamicsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Stability notions describe how nearby trajectories or perturbed systems behave relative to an invariant state, orbit, or set.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-math-stability-theorymit-ocw-nonlinear-dynamicsThis is an authored directed relation from the source endpoint to the target endpoint.
Stability theory classifies how trajectories near a fixed point behave; the fixed-point condition alone does not determine stability.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-math-fixed-pointwp-math-stability-theorymit-ocw-nonlinear-dynamicsThis is an authored directed relation from the source endpoint to the target endpoint.
Periodic orbits can be analyzed for orbital or transverse stability; periodicity alone does not imply attraction or stability.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-math-periodic-orbitwp-math-stability-theorymit-ocw-nonlinear-dynamicsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Lyapunov stability is the stability notion requiring sufficiently nearby initial states to remain nearby for all future time, without requiring attraction.
The target is a member or subtype of the broader source class.
wp-math-stability-theorymit-ocw-nonlinear-dynamics