Chirality is commonly associated with the spatial geometry of the atoms composing molecules, the biochemistry of living organisms, and spin properties. In sharp contrast, here we report chirality ...found in numerically computed stability diagrams of a chemical reaction governed by purely classical (that is, not quantum) equations, namely in a photochemically periodically perturbed ruthenium-catalyzed Belousov-Zhabotinsky reaction model. This novel chirality offers opportunities to explore hitherto unsuspected properties of purely classical chemical oscillators.
Clockwise and anticlockwise chiral walls of the BZ reaction.
Recently, an electro-kinetic model based on a specified reaction scheme for the electro-oxidation of formic acid on platinum was reported. The model evaluated three reaction pathways towards the ...production of CO
2
: the dehydrogenation and the dehydration of formic acid, and the third and most active pathway includes fast oxidation of the formate ion. Numerical integrations showed that the model is well-suited to describe the experimental results in voltammetric and oscillatory regimes. In the present paper, we provide detailed stability phase diagrams characterizing the dynamical evolution of this system under galvanostatic and potentiostatic regimes. We find the triple-pathway electro-oxidation of formic acid on platinum to have rather intertwined stability phases and, surprisingly, a total absence of chaotic oscillations. To the best of our knowledge, this is the first study in this direction using a realistic electrochemical model.
A detailed numerical study including stability phase diagrams for the dynamical evolution of the electro-oxidation of formic acid on platinum was reported. The study evidences the existence of intertwined stability phases and the absence of chaos.
We investigate the distribution of mixed-mode oscillations in the control parameter space for two paradigmatic chemical models: a three-variable fourteen-parameter model of the Belousov-Zhabotinsky ...reaction and a three-variable four-parameter autocatalator. For both systems, several high-resolution phase diagrams show that the number of spikes of their mixed-mode oscillations emerges consistently organized in a surprising and unexpected symmetrical way, forming Stern-Brocot trees. The Stern-Brocot tree is more general and contains the Farey tree as a subtree. We conjecture the Stern-Brocot hierarchical organization to be the archetypal skeleton underlying several systems displaying mixed-mode oscillations.
Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best ...strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.
Complexity of a peroxidase-oxidase reaction model Gallas, Jason A. C; Hauser, Marcus J. B; Olsen, Lars F
Physical chemistry chemical physics : PCCP,
01/2021, Letnik:
23, Številka:
3
Journal Article
Recenzirano
Odprti dostop
The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed ...mode oscillations. Here, we study a state-of-the-art model of the peroxidase-oxidase reaction. Using the model, we report systematic numerical experiments exploring the impact of changing the enzyme concentration on the dynamics of the reaction. Specifically, we report high-resolution phase diagrams predicting and describing how the reaction unfolds over a quite extended range of enzyme concentrations. Surprisingly, such diagrams reveal that the enzyme concentration has a huge impact on the reaction evolution. The highly intricate dynamical behaviours predicted here are difficult to establish theoretically due to the total absence of an adequate framework to solve nonlinearly coupled differential equations. But such behaviours may be validated experimentally.
The peroxidase-oxidase reaction was he first (bio)chemical reaction to show chaotic dynamics. Here, we show that the rich complex dynamics observed in a detailed model of the reaction changes dramatically with changes in enzyme concentration.
We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic ...progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.
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