Suppressed and Induced Chaos by Near Resonant Perturbation of Bifurcations

Vohra, S. T.; Fabiny, Larry; Bucholtz, F.

doi:10.1103/physrevlett.75.65

Cited by 38 publications

(22 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Experiments carried out on several lasers (YAG, fiber, CO 2 ) indicate that these methods are very general and consequently that this approach may be extended to other dynamical systems. In addition, the present work also provides an alternative explanation to the results obtained for the control of chaos by subharmonic modulation with extremely small detunings (near resonant perturbation) [Vohra et al, 1995] since such detunings may be considered as a slowly drifting phase and extreme care should be taken to separate e.g. detunings as small as 0.1 Hz with a basic resonance frequency of 10 kHz from the effects discussed in the present paper.…”

Section: Resultsmentioning

confidence: 71%

“…Chaos may also be controlled by adding a small modulation which is resonant or nearly resonant with a subharmonic of the fundamental system frequency [Meucci et al, 1994;Chizhevsky et al, 1986;Braiman & Goldhirsch, 1991;Colet & Braiman, 1996;Ciofini et al, 1995;Vohra et al, 1995]. This technique was first applied to a magnetostrictive ribbon and soon after to lasers including CO 2 [Meucci et al, 1994;Chizhevsky et al, 1986], microchip [Otsuka et al, 1997] and fiber [Dangoisse et al, 1997] lasers.…”

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Control of Chaos in Lasers by Feedback and Nonfeedback Methods

Glorieux

1998

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

Analytical approaches of the theory of chaos control in class B lasers are presented in the cases of continuous delayed feedback and of subharmonic modulation. They are compared with experimental findings on a CO 2 laser and a Nd-doped fiber laser with modulated loss and pump respectively. In both cases, analytical theory allows one to predict the shift of the first period-doubling bifurcations. Numerical simulations show that subharmonic modulation may induce shifts, crises and new attractors in a laser with modulated parameters and that its phase relative to the main modulation allows one to control the laser dynamics. These results agree well with the experimental observations on control of chaos in CO 2 and fiber lasers.

show abstract

Section: Resultsmentioning

confidence: 71%

Section: Introductionmentioning

confidence: 97%

Control of Chaos in Lasers by Feedback and Nonfeedback Methods

Glorieux

1998

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

show abstract

“…Such kind of perturbation has been proved to be efficient to stabilize linearly unstable periodic orbits. It has been used in systems with few degrees of freedom [25,26] as well as in solitons [27] and even in experiments [28]. In our case we achieve to lower the onset of the resonant steps significantly.…”

Section: The Effects Of Subharmonic Perturbations Of the Driving Fmentioning

confidence: 61%

Mode-locking of mobile discrete breathers

et al. 2005

View full text Add to dashboard Cite

We study numerically synchronization phenomena of mobile discrete breathers in dissipative nonlinear lattices periodically forced. When varying the driving intensity, the breather velocity generically locks at rational multiples of the driving frequency. In most cases, the locking plateau coincides with the linear stability domain of the resonant mobile breather and the desynchronization occurs by regular appearance of type I intermittencies. However, some plateaux also show chaotic mobile breathers with locked velocity in the locking region. The addition of a small subharmonic driving tames the locked chaotic solution and enhances the stability of resonant mobile breathers.

show abstract

“…The near-resonant perturbation of a system close to a bifurcation point can sometimes suppress or induce the bifurcation to chaos i.e. move the bifurcation point (e.g Lima and Pettini, 1990;Vohra et al, 1995). We speculate that the same may be happening here and thus the torus like behaviour may be found for larger values of F in the forced system than in the unforced one.…”

Section: The Travelling Wave Regimementioning

confidence: 81%

“…For example, previous workers have suppressed chaos using perturbation frequencies that are rational multiples of periodic drive frequencies that initiated the chaos (e.g. Braimin and Goldhirsch, 1991;Fronzoni et al, 1991;Vohra et al, 1995), or frequencies corresponding to peaks in the power spectrum of the undriven system (e.g. Sätherblom, 1997;Ding et al, 1994).…”

Section: Unstable Periodic Orbitsmentioning

confidence: 99%

Synchronization and chaos control in a periodically forced quasi-geostrophic two-layer model of baroclinic instability

Eccles

Read

Haine

2006

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract.Cyclic forcing on many timescales is believed to have a significant effect on various quasi-periodic, geophysical phenomena such as El Niño, the Quasi-Biennial Oscillation, and glacial cycles. This variability has been investigated by numerous previous workers, in models ranging from simple energy balance constructions to full general circulation models. We present a numerical study in which periodic forcing is applied to a highly idealised, two-layer, quasi-geostrophic model on a β-plane. The bifurcation structure and (unforced) behaviour of this particular model has been extensively examined by Lovegrove et al. (2001) and Lovegrove et al. (2002). We identify from their work three distinct regimes on which we perform our investigations: a steady, travelling wave regime, a quasi-periodic, modulated wave regime and a chaotic regime. In the travelling wave regime a nonlinear resonance is found. In the periodic regime, Arnol'd tongues, frequency locking and a Devil's staircase is seen for small amplitudes of forcing. As the forcing is increased the Arnol'd tongues undergo a period doubling route to chaos, and for larger forcings still, the parameter space we explored is dominated by either period 1 behaviour or chaotic behaviour. In the chaotic regime we extract unstable periodic orbits (UPOs) and add the periodic forcing at periods corresponding to integer multiples of the UPO periods. We find regions of synchronization, similar to Arnol'd tongue behaviour but more skewed and centred approximately on these periods. The regions where chaos suppression took place are smaller than the synchronization regions, and are contained within them.

show abstract

Suppressed and Induced Chaos by Near Resonant Perturbation of Bifurcations

Cited by 38 publications

References 17 publications

Control of Chaos in Lasers by Feedback and Nonfeedback Methods

Control of Chaos in Lasers by Feedback and Nonfeedback Methods

Mode-locking of mobile discrete breathers

Synchronization and chaos control in a periodically forced quasi-geostrophic two-layer model of baroclinic instability

Contact Info

Product

Resources

About