Post date: Jun 9, 2014 3:14:57 AM
Limit cycles are oscillations of fixed amplitude and fixed period displayed by nonlinear systems without external excitation. E.g., the academic Van der Pol equation which has position dependent damping. The limit cycle is sustained by periodically releasing energy into and absorbing energy from the environment.
Real world examples: aircraft wing fluttering, hopping in legged robots, electrical circuits, some earth moving excavators, etc.
Linear systems also exhibit oscillations when the poles are on the imaginary axis (marginally stable). But in contrast to limit cycles, the oscillatory response of a marginally stable linear system will have its amplitude dependent on the initial conditions. Some parametric changes can also shift the poles, and make the system unstable or more stable. Limit cycles in nonlinear systems are not easily affected by parameter changes.