For different settings of a control parameter, a chaotic system can go from a region with two separate stable attractors (generalized bistability) to a crisis where a chaotic attractor expands, colliding with an unstable orbit. In the bistable regime jumps between independent attractors are mediated by external perturbations; above the crisis, the dynamics includes visits to regions formerly belonging to the unstable orbits and this appears as random bursts of amplitude jumps. We introduce a control method which suppresses the jumps in both cases by filtering the specific frequency content of one of the two dynamical objects. The method is tested both in a model and in a real experiment with a CO2 laser.

By tuning a control parameter, a chaotic system can either display two or more attractors (generalized multistability) or exhibit an interior crisis, whereby a chaotic attractor suddenly expands to include the region of an unstable orbit (bursting regime).Recently, control of multistability and bursting have been experimentally proved in a modulated class B laser by means of a feedback method. In a bistable regime, the method relies on the knowledge of the frequency components of the two attractors. Near an interior crisis, the method requires retrieval of the unstable orbit colliding with the chaotic attractor.We also show that a suitable parameter modulation is able to control bistability in the Lorenz system. We observe that, for every given modulation frequency, the chaotic attractor is destroyed under a boundary crisis. The threshold control amplitude depends on the control frequency and the location of the operating point in the bistable regime. Beyond the boundary crisis, the system remains in the steady state even if the control is switched off, demonstrating control of bistability.

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We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.