Avoiding escapes in open dynamical systems using phase control

Year: 2008

Authors: Seoane J.M., Zambrano S., Euzzor S., Meucci R., Arecchi F.T., Sanjuán M.A.F.

Autors Affiliation: Nonlinear Dynamics and Chaos Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain;
CNR – Istituto Nazionale di Ottica Applicata, Largo E. Fermi, 6 50125 Firenze, Italy;
Department of Physics, Università di Firenze, Firenze, Italy

Abstract: In this paper we study how to avoid escapes in open dynamical systems in the presence of dissipation and forcing, as it occurs in realistic physical situations. We use as a prototype model the Helmholtz oscillator, which is the simplest nonlinear oscillator with escapes. For some parameter values, this oscillator presents a critical value of the forcing for which all particles escape from its single well. By using the phase control technique, weakly changing the shape of the potential via a periodic perturbation of suitable phase phi, we avoid the escapes in different regions of the phase space. We provide numerical evidence, heuristic arguments, and an experimental implementation in an electronic circuit of this phenomenon. Finally, we expect that this method might be useful for avoiding escapes in more complicated physical situations.

Journal/Review: PHYSICAL REVIEW E

Volume: 78 (1)      Pages from: 016205  to: 016205

KeyWords: Dynamical systems; Electron tubes; Networks (circuits); Phase control; Phase space methods; Schrodinger equation, American Physical Society (APS); Control techniques; Critical values; Helmholtz; Non-linear oscillators; Numerical evidence; Open dynamical systems; Parameter values; Periodic perturbations; Phase spaces; Prototype models, Control systems
DOI: 10.1103/PhysRevE.78.016205

ImpactFactor: 2.508
Citations: 30
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