Inverse Ruelle–Takens–Newhouse scenario in a closed unstirred cerium-catalysed Belousov–Zhabotinsky system

Rustici, Mauro; Branca, Mario; Brunetti, Antonio; Caravati, Carlo; Marchettini, Nadia

doi:10.1016/s0009-2614(98)00781-7

Cited by 15 publications

(12 citation statements)

References 19 publications

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“…For A = 0.021 ( Figure 5c ), complex substructures, which show the torus break up being replaced by strange attractors (A/S′ = 0.76) can be observed in the Poincare section and in the power spectra. This route to chaos is also called the Ruelle-Takens-Newhouse route [ 294 , 296 ].…”

Section: Effect Of the Delays On Temporal Self-organizationsmentioning

confidence: 99%

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

Fuente

2010

IJMS

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One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

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Section: Effect Of the Delays On Temporal Self-organizationsmentioning

confidence: 99%

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

Fuente

2010

IJMS

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“…Similarly, the region T2 describes an inverse RTN scenario. 13,17 In stirred reactors, the BZ dynamics can be driven to chaos just by modifying kinetic parameters (temperature, reagents concentration, mean residence time, etc. ), while in batch reactors the coupling among kinetics and transport phenomena plays a fundamental role.…”

Section: Introductionmentioning

confidence: 99%

“…[24][25][26][27] The kinetics obviously influences the oscillatory dynamics even in batch unstirred reactors, 12,28 but so far its role has not been fully understood. In the past, 15,17,28 we speculated that the transition T2, from chaos to periodicity, could be driven by the reagents consumption. In this paper we model this behavior by modifying the Oregonator kinetic equations 29,30 in order to include the consumption of the main reagents, namely malonic acid (MA) and bromate ions (BrO À 3 ).…”

Section: Introductionmentioning

confidence: 99%

Role of the reagents consumption in the chaotic dynamics of the Belousov–Zhabotinsky oscillator in closed unstirred reactors

Marchettini

Budroni

Rossi

et al. 2010

Phys. Chem. Chem. Phys.

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Chemical oscillations generated by the Belousov-Zhabotinsky reaction in batch unstirred reactors, show a characteristic chaotic transient in their dynamical regime, which is generally found between two periodic regions. Chemical chaos starts and finishes by following a direct and an inverse Ruelle-Takens-Newhouse scenario, respectively. In previous works we showed, both experimentally and theoretically, that the complex oscillations are generated by the coupling among the nonlinear kinetics and the transport phenomena, the latter due to concentration and density gradients. In particular, convection was found to play a fundamental role. In this paper, we develop a reaction-diffusion-convection model to explore the influence of the reagents consumption (BrO in particular) in the inverse transition from chaos to periodicity. We demonstrated that, on the route towards thermodynamic equilibrium, the reagents concentration directly modulates the strength of the coupling between chemical kinetics and mass transport phenomena. An effective sequential decoupling (reaction-diffusion-convection --> reaction-diffusion --> reaction) takes place upon the reagents consumption and this is at the basis of the transition from chaos to periodicity.

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“…1,2 Among these, chaotic attractors, (multi-)fractals, self-assemblies, dissipative structures and self-organization represent some of the most promising recent concepts. A particularly important testbed for a conceptualization of pattern formation in self-organizing systems is the B-Z reaction [3][4][5][6][7][8][9] which belongs among the most extensively studied examples of chemical self-organization. However, despite decades of intensive research, there are still ongoing controversies over the actual chemical kinetics (i.e.…”

Section: Introductionmentioning

confidence: 99%

Noisy hodgepodge machine and the observed mesoscopic behavior in the non-stirred Belousov–Zhabotinsky reaction

Štys

Rychtáriková

Zhyrova

et al. 2019

Eur. Phys. J. Spec. Top.

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Mesoscopic dynamics of self-organized structures is the most important aspect in the description of complex living systems. The Belousov-Zhabotinsky (B-Z) reaction is in this respect a convenient testbed because it represents a prototype of chemical self-organization with a rich variety of emergent wave-spiral patterns. Using a multi-state stochastic hotchpotch model, we show here that the mesoscopic behaviour of the non-stirred B-Z reaction is both qualitatively and quantitatively susceptible to the description in terms of stochastic multilevel * To whom correspondence should be addressed † ICPF ‡ FJFI 1 arXiv:1602.03055v1 [nlin.CG] 6 Feb 2016 cellular automata. This further implies that the mesoscopic dynamics of the non-stirred B-Z reaction results from a delicate interplay between a) a maximal number of available states within the elementary time lag (i.e. a minimal time interval needed for demise of a final state) and b) an imprecision or uncertainty in the definition of state. If either the number of time lags is largely different from 7 or the maximal number of available states is smaller than 20, the physicochemical conditions are inappropriate for a formation of the wave-spiral patterns.Furthermore, a white noise seems to be key for the formation of circular structures (target patterns) which could not be as yet systematically explained in existing models.

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Inverse Ruelle–Takens–Newhouse scenario in a closed unstirred cerium-catalysed Belousov–Zhabotinsky system

Cited by 15 publications

References 19 publications

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

Role of the reagents consumption in the chaotic dynamics of the Belousov–Zhabotinsky oscillator in closed unstirred reactors

Noisy hodgepodge machine and the observed mesoscopic behavior in the non-stirred Belousov–Zhabotinsky reaction

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