Stability

Stability describes how a dynamical system responds when its state is perturbed from an equilibrium.

Stable behaviour

An equilibrium is stable if trajectories starting sufficiently close remain close. It is asymptotically stable if nearby trajectories also return toward the equilibrium as time increases.

Unstable behaviour

An equilibrium is unstable if arbitrarily small disturbances can lead trajectories away from it.

Local and global stability

Local stability concerns behaviour near an equilibrium. Global stability asks whether a much larger set of initial conditions approaches the same equilibrium.