Attractor Selection in Chaotic Dynamics

Abstract

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.

Amplitude-Phase Synchronization at the Onset of Permanent Spatiotemporal Chaos

“…Experimental evidence of chaotic saddles has been obtained in lasers [2] and pipe flows [3]. Numerical simulations of turbulent shear flows have observed a turbulent flow behaving as a chaotic saddle coexisting with a laminar flow separated by an edge of chaos [4].…”

Alfvén multistability: Transient and intermittent dynamics induced by noise

“…Finally, we stress that knowledge of the different attractors and chaotic saddles of a system opens the possibility of using control techniques to suppress the random bursts of amplitude jumps in the intermittent regime, as recently shown by Meucci et al 33 for a model and in a real experiment with a CO 2 laser. Such technology may be of interest for turbulence control in confined plasmas.…”

Control and synchronization of laser bursting and its implications in neuroscience

“…3a, b giving evidence of burst suppression; on the contrary it is enhanced for a positive feedback in Fig. 3c, d (Meucci et al 2005). The control of irregular bursting was investigated by Elson et al (1999) in the Lateral Pyloric neuron (LP) of the Central Pattern Generator (CPG) of the lobster stomatogastric ganglion.…”