Finding limit cycles in general is a very difficult problem.

A limit cycle cannot exist in fewer than two dimensions.

Instead, after sufficient time, the oscillations approach a limit cycle.

Two simple attractors are a fixed point and the limit cycle.

We see this as a deviation from the nominal limit cycle.

On the other hand, when , is also positive, and the system will give rise to a limit cycle.

This behaviour appears as a stable limit cycle of the equations describing the model.

In the non-linear system's response, this translates into an end to the stable limit cycle.

The Goodwin model, though, shows no stable limit cycles.

They may exhibit properties such as limit cycle, bifurcation, chaos.

Quadratic plane vector fields with four limit cycles are known.

We have evaluated the degree to which this limit cycle is robust to variations in all the system parameters.

Trajectories leading to a sink and a limit cycle are illustrated in Fig. 2.1.

Liénard's Theorem can be used to prove that the system has a limit cycle.

Here the stable limit cycle is shown in state space as a closed orbit (the ellipse).

The existence and stability of these limit cycles may change under parametric perturbations.

Depending on the particular form of the limit cycle, a small finite number of coefficients can be used.

Because recycling materials required new infrastructure as well as transportation resources, there was limited cycle development.

There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle.

The second criterion requires that when , there exists a stable limit cycle solution.

Limit cycle, trophic function and the dynamics of intersectoral interaction.

In a continuous-flow reactor, this becomes a closed loop (limit cycle).

Homoclinic bifurcation in which a limit cycle collides with a saddle point.

When , has a stable limit cycle solution.

When perturbed, the oscillator responds by spiraling back into the limit cycle.