Control of Turing pattern formation by delayed feedback.
ABSTRACT The effect of the global delayed feedback technique on Turing pattern formation is investigated in the modified Lengyel-Epstein two-variable model. Feedback intensity, delay time, and feedback-imposing time (the period of time that feedback is present in the system) are all found to be of significant influence on Turing pattern formation time. Under appropriate parameter settings, delayed feedback could suppress or induce the Turing pattern if the feedback intensity is strong enough.
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ABSTRACT: We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatiotemporal forcing in the form of a traveling-wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally modulated traveling waves and localized traveling solitonlike solutions. The latter make contact with the soliton solutions of Coullet [Phys. Rev. Lett. 56, 724 (1986)]] and generalize them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive chlorine dioxide-iodine-malonic acid reaction are also reported.Physical Review Letters 04/2003; 90(12):128301. · 7.94 Impact Factor
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ABSTRACT: Effects of global delayed feedback on diffusion-induced turbulence are studied in a realistic model of catalytic oxidation of carbon monoxide on Pt(110). Spatiotemporal patterns resulting from numerical simulations of this model are identified and analyzed using a transformation into the phase and the amplitude of local oscillations. We find that chemical turbulence can be efficiently controlled by varying the feedback intensity and the delay time in the feedback loop. Near the transition from turbulence to uniform oscillations, various chaotic and regular spatiotemporal patterns-intermittent turbulence, two-phase clusters, cells of hexagonal symmetry, and phase turbulence-are found.Physical Review E 04/2003; 67(3 Pt 2):036207. · 2.31 Impact Factor
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ABSTRACT: We study the dynamics of an array of single mode semiconductor lasers globally but weakly coupled by a common external feedback mirror and by nearest neighbor interactions. We seek to determine the conditions under which all lasers of the array are in phase, whether in a steady, periodic, quasiperiodic, or chaotic regime, in order to maximize the output far field intensity. We show that the delay may be a useful control parameter to achieve in-phase synchronization. For the in-phase steady state, there is a competition between a delay-induced Hopf bifurcation leading to an in-phase periodic regime and a delay-independent Hopf bifurcation leading to an antiphased periodic regime. Both regimes are described analytically and secondary Hopf bifurcations to quasiperiodic solutions are found. Close to the stable steady state, the array is described by a set of Kuramoto equations for the phases of the fields. Above the first Hopf bifurcation, these equations are generalized by the addition of second and third order time derivatives of the phases.Physical Review E 08/2001; 64(1 Pt 2):016613. · 2.31 Impact Factor