Clusters and Switchers in Globally Coupled Photochemical Oscillators

Taylor, Annette F.; Kapetanopoulos, Panagiotis; Whitaker, Benjamin J.; Tóth, Rita; Bull, Larry; Tinsley, Mark R.

doi:10.1103/physrevlett.100.214101

Cited by 43 publications

(45 citation statements)

References 32 publications

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“…The chemical micro-oscillators used in this study are catalyst-loaded cation-exchange beads in a catalyst-free BZ reaction mixture 10,18,[31][32][33] . To increase oscillator homogeneity, the particles (DOWEX WX4 100-200, diameters 75-150 μ m) were sieved to obtain a narrow size distribution of 106-112 μ m. The rutheniumtris-dimethylene-bipyridine ( + Ru(dmbpy) 3 2 ) catalyst was slowly added to 5.0 ml water containing 1.0 g of doubly-sieved beads and stirred with a vortex mixer for one day.…”

Section: Methodsmentioning

confidence: 99%

“…We used the non-dimensionalized ZBKE model 10,28,31 (see Supplementary Section 'Numerical models') with a rectangular distribution in the parameter q ∈ [0.6, 0.8] that leads to a heterogeneous period distribution with a standard deviation of 4.4% of the mean period. Nonlocal coupling was applied to each oscillator via the model parameter I j,k in a similar manner to equation (1), but with the measured greyscale value g j,k replaced by the oxidized catalyst concentration of the model.…”

Section: Grey Valuementioning

confidence: 99%

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Spiral wave chimera states in large populations of coupled chemical oscillators

et al. 2017

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Section: Methodsmentioning

confidence: 99%

Section: Grey Valuementioning

confidence: 99%

Spiral wave chimera states in large populations of coupled chemical oscillators

et al. 2017

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“…The illumination generates the excited form of the reduced catalyst, RuðbpyÞ 2þÃ 3 , which initiates a sequence of photochemical reactions that produce the autocatalyst HBrO 2 [19,22,24,25].…”

Section: Methodsmentioning

confidence: 99%

“…We therefore developed an oscillator array that permits the simultaneous perturbing and coupling of over 1000 oscillators. (Our previous studies of photochemically coupled BZ oscillators have been limited to approximately 40 oscillators [19][20][21][22][23].) In the oscillator array, the photosensitive oscillators are catalyst-loaded beads of about 200 μm in diameter, each of which is fixed on a film of polydimethylsiloxane (PDMS), which is then positioned in an open reactor that is continually replenished with a catalyst-free BZ solution.…”

Section: Methodsmentioning

confidence: 99%

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Echo Behavior in Large Populations of Chemical Oscillators

et al. 2016

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Experimental and theoretical studies are reported, for the first time, on the observation and characterization of echo phenomena in oscillatory chemical reactions. Populations of uncoupled and coupled oscillators are globally perturbed. The macroscopic response to this perturbation dies out with time: At some time τ after the perturbation (where τ is long enough that the response has died out), the system is again perturbed, and the initial response to this second perturbation again dies out. Echoes can potentially appear as responses that arise at 2τ; 3τ; ... after the first perturbation. The phase-resetting character of the chemical oscillators allows a detailed analysis, offering insights into the origin of the echo in terms of an intricate structure of phase relationships. Groups of oscillators experiencing different perturbations are analyzed with a geometric approach and in an analytical theory. The characterization of echo phenomena in populations of chemical oscillators reinforces recent theoretical studies of the behavior in populations of phase oscillators [E. Ott et al., Chaos 18, 037115 (2008)]. This indicates the generality of the behavior, including its likely occurrence in biological systems.

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Engineering of Synchronization and Clustering of a Population of Chaotic Chemical Oscillators

et al. 2011

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Description, control, and design of weakly interacting dynamical units are challenging tasks that play a central role in many physical, chemical, and biological systems. [1][2][3][4][5] Control of temporal and spatial variations of reaction rates is especially daunting when the dynamical units exhibit deterministic chaotic oscillations that are sensitive to initial conditions and are long-term unpredictable. Control of spatiotemporal chaos by means of suppression of spiralwave turbulence to standing waves, cluster patterns, and uniform periodic oscillations, in the catalytic CO oxidation on a Pt (110) single-crystal surface has been successfully achieved with linear delayed feedback of the carbon monoxide partial pressure.[6] The same delayed global feedback methodology has also been applied to induce various dynamical clusters in electrochemical corrosion processes [7] and in the light-sensitive Belousov-Zhabotinsky (BZ) reaction.[8] A fundamental problem of tuning the complex structure of chaotic systems is choosing a feedback scheme and appropriate control parameters to steer the system to a desired structure of spatiotemporal reactivity. This objective requires the use of simple yet accurate models of nonlinear processes, their interactions, and responses to external perturbations. When the individual units exhibit periodic oscillatory behavior, the effect of weak feedback and coupling can be described by phase models [4,9] in which the state of each unit is represented by a single variable, the phase of oscillations.Typical phase-synchronized behavior of a population of periodic oscillators is dynamical differentiation (clustering) where the elements form groups (clusters) in which the phases are identical at all times but different from the phases of the elements in the other groups.[9]Phase models successfully described synchronization and dynamical differentiation (clustering) of oscillatory electrochemical [10] and BZ bead experiments.[11] Experiment-based phase models can also be used for synchronization engineering of periodic oscillators [12] where a carefully designed external feedback is applied to dial-up complex dynamical structures such as stable and sequentially visited dynamical cluster patterns and desynchronization.Herein, we consider populations of chaotic oscillators that exhibit strong cycle-to-cycle period variations. We show that the feedback scheme can be designed to obtain dynamical synchronization states of phase coherent chaotic oscillators in a quantitative manner. The method relies on the flexibility and versatility of synchronization engineering (originally developed for periodic oscillators [12] ) and on the observation that the long-term phase dynamics of chaotic oscillators is often similar to that of noisy periodic oscillators. [13] An experimental system of uncoupled, phase-coherent, chaotic oscillators was constructed by using an electrochemical cell consisting of 64 Ni working electrodes (99.98 % pure), a Pt mesh counter electrode, and a Hg/Hg 2 SO 4 /K 2 SO 4 (saturated) r...

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Clusters and Switchers in Globally Coupled Photochemical Oscillators

Cited by 43 publications

References 32 publications

Spiral wave chimera states in large populations of coupled chemical oscillators

Spiral wave chimera states in large populations of coupled chemical oscillators

Echo Behavior in Large Populations of Chemical Oscillators

Engineering of Synchronization and Clustering of a Population of Chaotic Chemical Oscillators

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