Library Concept
Limit cycle
An isolated closed trajectory in a dynamical system's phase space that nearby states spiral toward, or away from — the mathematical signature of a stable, self-sustaining oscillation.
In a dynamical system’s phase space, an isolated closed trajectory that neighboring trajectories spiral toward (a stable limit cycle) or away from (unstable) — the mathematical signature of a self-sustaining oscillation that returns to the same periodic path regardless of small perturbations. Henri Poincaré introduced the concept in 1882; the standard physical example is the Van der Pol oscillator, Balthasar van der Pol’s 1920s model of self-sustaining oscillation in a vacuum-tube triode circuit, which settles into the same stable cycle from a wide range of starting conditions.