Scientific Results

Attractor selection in a modulated laser and in the Lorenz circuit

Year: 2008

Authors: Meucci R., Salvadori F., Al Naimee K., Brugioni S., Goswami B.K., Boccaletti S., Arecchi F.T.

Autors Affiliation: CNR—Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy;
Department of Physics, University of Florence, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy;
Department of Physics, College of Sciences, University of Baghdad, PO Box 47322, Jadiryah, Baghdad, Iraq;
Laser and Plasma Technology Division, Bhabha Atomic Research Centre, Mumbai 400 085, India;
CNR — Istituto dei Sistemi Complessi, Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy

Abstract: 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.


Volume: 366 (1864)      Pages from: 475  to: 486

KeyWords: Bursting; Control of chaos; Generalized multistability; Boundary layers; Lorentz force; Networks (circuits), Chaotic attractor; Control parameter; Frequency components; Generalized multistability; Lorenz system, Chaotic systems
DOI: 10.1098/rsta.2007.2104

Citations: 2
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