Analysis of complex oscillatory dynamics of a pH oscillator

Bakeš, D.; Schreiberová, Lenka; Schreiber, Igor; Hauser, M.

doi:10.1134/s0036024407090117

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…Due to its complex mechanism, the H 2 O 2 -S 2 O 3 2--H 2 SO 4 -Cu 2+ reaction displays a rich variety of dynamical regimes including three different steady states, simple periodic and mixed-mode periodic oscillations, 9 and recently reported mixedmode chaotic and quasiperiodic regimes. 22 When arranged into bifurcation diagrams as presented by Orba ´n and Epstein 9 and in this work, the regions of steady states and oscillations form a structure partly resembling a cross-shaped diagram. We used the mechanism proposed by Kurin-Cso ¨rgei et al 17 and optimized the values of adjustable parameters by successively constructing bifurcation diagrams with the aim of achieving best possible agreement with experiments.…”

Section: Discussionsupporting

confidence: 53%

“…Due to its complex mechanism, the H 2 O 2 −S 2 O 3 2- −H 2 SO 4 −Cu 2+ reaction displays a rich variety of dynamical regimes including three different steady states, simple periodic and mixed-mode periodic oscillations, and recently reported mixed-mode chaotic and quasiperiodic regimes . When arranged into bifurcation diagrams as presented by Orbán and Epstein 9 and in this work, the regions of steady states and oscillations form a structure partly resembling a cross-shaped diagram.…”

Section: Discussionsupporting

confidence: 53%

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Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu²⁺ Reaction

et al. 2008

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The hydrogen peroxide-thiosulfate-Cu2+ reaction operated in a continuous flow stirred tank reactor is a pH-oscillator known to provide three different steady states, hysteresis, and oscillations. In addition to the various dynamical regimes established earlier, a question arises whether the reaction can be also excitable, whereby the system strongly responds to a small but supercritical external addition of certain chemical species. We carried out experiments aimed at finding excitability and studying response dynamics to single and repeated pulsed perturbations of varying amplitude and period. We found that the reaction displays a remarkable excitatory dynamics when forced. The available mechanism of the reaction involves several adjustable parameters, which need to be tuned so that the model corresponds to experimentally observed bifurcation diagrams. Our experimental findings are compared with numerical calculations, suggesting that the model is far from complete.

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Section: Discussionsupporting

confidence: 53%

Section: Discussionsupporting

confidence: 53%

Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu²⁺ Reaction

et al. 2008

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“…Since the oscillations and bistability occur at low levels of enzyme, these behaviours are expected to be more difficult to reproduce without precise knowledge of the enzyme activity in a given experimental run. Bistability was also obtained in a flow reactor with glucose oxidase that was later difficult to reproduce . Precise characterization of enzyme activity in stock solutions is essential if the range of parameters for which dynamical behaviour is obtained is narrow.…”

Section: Feedback‐driven Behaviormentioning

confidence: 99%

“…Bistability was also obtained in a flow reactor with glucose oxidase that was later difficult to reproduce. [50] Precise characterization of enzyme activity in stock solutions is essential if the range of parameters for which dynamical behaviour is obtained is narrow. Alternatively, methods must be sought for increasing the oscillatory domain in phase space for robust oscillations with the pH-driven feedback mechanism.…”

Section: Feedback-driven Behaviormentioning

confidence: 99%

Exploitation of Feedback in Enzyme‐catalysed Reactions

Bánsági

Taylor

2018

Israel Journal of Chemistry

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Some cellular systems, such as yeast, bacteria and slime mould, display dynamic behavior including switches and rhythms driven by feedback in enzyme‐catalysed reactions. The mechanisms of these processes have been well investigated and recent attention has turned to generating similar responses in synthetic biocatalytic systems, with a view to creating bioinspired analogues for applications. Here we discuss how feedback arises in the reaction mechanisms of some enzyme‐catalyzed reactions in vitro, the behaviour obtained and the emerging applications. These autocatalytic reactions may provide insights into behaviour in cellular systems as well as new methods for drug delivery, sensing and repair that can be exploited in living systems.

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Mixed-mode oscillations in a homogeneous p H-oscillatory chemical reaction system

Bakeš

Schreiberová

Schreiber

et al. 2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We examine experimentally a chemical system in a flow-through stirred reactor, which is known to provide large-amplitude oscillations of the pH value. By systematic variation of the flow rate, we find that the system displays hysteresis between a steady state and oscillations, and more interestingly, a transition to chaos involving mixed-mode oscillations. The basic pattern of the measured pH in the mixed-mode regime includes a large-scale peak followed by a series of oscillations on a much smaller scale, which are usually highly irregular and of variable duration. The bifurcation diagram shows that chaos sets in via a period-doubling route observed on the large-amplitude scale, but simultaneously small-amplitude oscillations are involved. Beyond the apparent accumulation of period doubling bifurcations, a mixed-mode regime with irregular oscillations on both scales is observed, occasionally interrupted by windows of periodicity. As the flow rate is further increased, chaos turns into quasiperiodicity and later to a simple small-amplitude periodic regime. Dynamics of selected typical regimes were examined with the tools of nonlinear time-series analysis, which include phase space reconstruction of an attractor and calculation of the maximal Lyapunov exponent. The analysis points to deterministic chaos, which appears via a period doubling route from below and via a route involving quasiperiodicity from above, when the flow rate is varied.

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Analysis of complex oscillatory dynamics of a pH oscillator

Cited by 4 publications

References 24 publications

Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu²⁺ Reaction

Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu²⁺ Reaction

Exploitation of Feedback in Enzyme‐catalysed Reactions

Mixed-mode oscillations in a homogeneous p H-oscillatory chemical reaction system

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Analysis of complex oscillatory dynamics of a pH oscillator

Cited by 4 publications

References 24 publications

Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu2+ Reaction

Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu2+ Reaction

Exploitation of Feedback in Enzyme‐catalysed Reactions

Mixed-mode oscillations in a homogeneous p H-oscillatory chemical reaction system

Contact Info

Product

Resources

About

Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu²⁺ Reaction

Response Dynamics to Pulsed Perturbations of the Hydrogen Peroxide−Thiosulfate−Cu²⁺ Reaction