Limit cycle
A limit-cycle is a closed trajectory in phase space exhibited by nonlinear systems. As a dynamical system evolves, its trajectory might tend to spiral in towards a closed loop in the phase space. The neighboring trajectories may either spiral towards the limit-cycle or move away from it. In the case where all the neighboring trajectories move towards the limit-cycle, it is called a stable limit-cycle. Otherwise it is an unstable limit-cycle.
Stable limit-cycles imply self-sustained oscillations. Any small perturbation from the closed trajectory would cause the system to return to the limit-cycle, making the system stick to the limit-cycle.
Figure illustrating a stable limit cycle for the
