Controlling chaos in the Belousov—Zhabotinsky reaction

Petrov, Valery; Gáspár, Vilmos; Masere, Jonathan; Showalter, Kenneth

doi:10.1038/361240a0

Cited by 386 publications

(183 citation statements)

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“…Among them, we here recall (besides OGY) the so called occasional proportional feedback (OPF) simultaneously introduced by Hunt [15] and Showalter [17], the method of Huebler [58], and the method introduced by Pyragas [2], which apply a delayed feedback on one of the system variables. All these methods are model independent, in the sense that the knowledge on the system necessary to select the perturbation can be done by simply observing the system for a suitable learning time.…”

Section: The Basic Ideamentioning

confidence: 99%

“…The most popular chaotic chemical system is the Belousov}Zhabotinsky (BZ) reaction, where a cerium ion-catalyzed oxidation malonic acid is produced by acidi"ed bromate [149] in a continuous-#ow stirred-tank reactor. The "rst control experiment in chemical chaos was implemented in a BZ reaction by the group of Showalter [17]. The authors here applied the so called single map based algorithm to an oscillatory BZ reaction continuously excited, feedbacking the control signal` a of the cerium and bromide solutions entering the reaction tank.…”

Section: Control Of Chemical Chaosmentioning

confidence: 99%

“…[4}8]. In face of this huge number of theoretical studies, experimental realizations of chaos control have been achieved with a magnetoelastic ribbon [9], a heart [10,11], a thermal convection loop [12,13], a yttrium iron garnet oscillator [14], a diode oscillator [15], an optical multimode chaotic solid-state laser [16], a Belousov}Zhabotinski reaction di!usion chemical system [17], and many other experiments.…”

Section: From the Ott}grebogi}yorke Ideas And Technique To The Other mentioning

confidence: 99%

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The control of chaos: theory and applications

et al. 2000

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Section: The Basic Ideamentioning

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Section: Control Of Chemical Chaosmentioning

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Section: From the Ott}grebogi}yorke Ideas And Technique To The Other mentioning

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The control of chaos: theory and applications

et al. 2000

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“…In particular, the stabilization and control of various patterns [3][4][5][6][7][8][9] through local, nonlocal, or global feedback, and pattern formation in media with designed heterogeneities [10 -12] are the source of novel insights for spatiotemporal dynamics.…”

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confidence: 99%

Gentle Dragging of Reaction Waves

et al. 2003

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Using a recently realized ''addressable catalyst surface'' [Science 294, 134 (2001)] we study the interaction of chemical reaction waves with prescribed spatiotemporal fields. In particular, we study how a traveling chemical pulse is ''dragged'' by a localized, moving temperature heterogeneity as a function of its intensity and speed. The acceleration and eventual ''detachment'' of the wave from the heterogeneity is also explored through simulation and stability analysis. DOI: 10.1103/PhysRevLett.90.018302 PACS numbers: 82.40.Bj, 05.45.-a, 82.40.Np, 82.45.Jn As the elements of spontaneous pattern formation are progressively understood through theory, experimentation, and scientific computation [1], ways to purposefully interact with the coherent structures (pulses and fronts) that constitute the building blocks of spatiotemporal patterns are becoming the focus of extensive research [2,3]. In particular, the stabilization and control of various patterns [3-9] through local, nonlocal, or global feedback, and pattern formation in media with designed heterogeneities [10 -12] are the source of novel insights for spatiotemporal dynamics.To explore such phenomena, we have recently constructed an ''addressable catalyst'': A focused laser beam, manipulated through computer-controlled mirrors and capable of ''writing'' spatiotemporal temperature heterogeneity patterns on a metal single crystal catalyst. The loop between this actuation and sensing (both resolved in space and time) through nonintrusive microscopies is then closed through the computer or the experimentalist herself/himself in real time. Our model system is the low-pressure catalytic oxidation of CO on Pt(110), a reaction exhibiting well-documented spatiotemporal patterns [13][14][15][16], and whose macroscopic modeling has reached an advanced level [17][18][19][20].In this Letter we study the interaction of reactive pulses with a single, spatially coherent but temporally mobile heterogeneity. In particular, we use a temperature heterogeneity, localized in space and steadily moving in time, to ''drag'' spontaneously isothermally forming reactive pulses and fronts with speeds differing from their natural speed. We examine the shapes acquired by these dragged waves and their limits of stability (that is, the range of dragging speeds for which they can exist). Through computer-aided analysis we examine the nature of the detachment instability, marking the loss of the ability of the heterogeneity to drag a pulse in 1D or 2D. Two possible paths to instability (depending on the linearized spectrum crossing) are detected. We explore the postdetachment transient dynamics and the interactions of a pulse with successive elements of a 1D periodic, constant speed array of identical heterogeneities. The theme of pulse dragging is currently also being explored in a variety of physically relevant Hamiltonian systems, or weakly perturbed dissipative variations thereof (targeted transfer of pulses in optical media or the motion/displacement of harmonic traps or optical l...

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“…[20][21][22][23]). Whereas the control of UPOs has been very successful for slow systems (characteristic time scale > 1 µs) [24][25][26][27], applying feedback control to fast chaotic systems is challenging because the controller requires a finite time to sense the current state of the system, determine the appropriate perturbation, and apply it to the system. This finite time interval, often called the control-loop latency τ , can be problematic if the state of the system is no longer correlated with its measured state at the time when the perturbation is applied.…”

Section: Introductionmentioning

confidence: 99%