Stabilizing unstable orbits by slow modulation of a control parameter in a dissipative dynamic system

Stabilization of unstable periodic orbits embedded in chaotic or nonchaotic attractors is achieved by slow nonfeedback periodic modulation of a control parameter, without crossing bifurcation boundaries. Also, it is shown that a step change in the parameter inside one periodic regime can destabilize the system, bringing it to an unstable limit cycle dependent on the amplitude and phase of the parameter change. Periodic modulation of the control parameter with a period smaller than the average time spent on the unstable orbit stabilizes this orbit. The effect is demonstrated in a loss-driven [formula presented] laser with periodically modulated cavity detuning. The results of numerical simulations are in a good agreement with experimental results. © 1998 The American Physical Society.