Early models of chemical oscillations failed to provide bounded solutions

Erneux, Thomas

doi:10.1098/rsta.2017.0380

Cited by 7 publications

(6 citation statements)

References 35 publications

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“…It has been shown that the basic Selkov system admits solutions with unbounded oscillations and that the diameter of the image of a periodic solution can tend to infinity as approaches a finite limit, thus completing the results of Brechmann and Rendall ( 2018 ) on that system and rigorously confirming a claim made in Selkov ( 1968 ). Note that some statements related to this issue have been made in Erneux ( 2018 ) but that reference does not contain rigorous proofs of those statements. One remaining question is that of the rate with which the diameter of the image of the periodic solution tends to infinity as the critical parameter value is approached.…”

Section: Discussionmentioning

confidence: 99%

Unbounded solutions of models for glycolysis

Brechmann

Rendall

2021

J. Math. Biol.

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The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This is done with the help of a Poincaré compactification of the system and a shooting argument. This system was originally derived from another system with Michaelis–Menten kinetics. A Poincaré compactification of the latter system is carried out and this is used to show that the Michaelis–Menten system, like that with mass action, has solutions which diverge to infinity in a monotone manner. It is also shown to admit subcritical Hopf bifurcations and thus unstable periodic solutions. We discuss to what extent the unbounded solutions cast doubt on the biological relevance of the Selkov oscillator and compare it with other models for the same biological system in the literature.

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Section: Discussionmentioning

confidence: 99%

Unbounded solutions of models for glycolysis

Brechmann

Rendall

2021

J. Math. Biol.

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“…The Brusselator model consists of a single nonlinear (three molecules) reaction that describes the evolutionary process of two chemical intermediates X and Y [ 29 ]. The model is a mathematical model, which can be used to simulate the self-organizing phenomenon of a given system and identify whether the system achieves a dissipative structure accurately and rationally [ 30 ].…”

Section: Model and Datamentioning

confidence: 99%

An empirical analysis of social public resources digital sharing system: Dissipative structure theory

Jiang

2022

PLoS ONE

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The development of the social public resource digital sharing system (SPRDSS) has been accelerated with the evolution of digital information and communication technologies (ICTs). This paper analyzes the dissipative structure features and formation process of SPRDSS in China. Combined with the Brusselator model and its transformation, this paper empirically analyzes the dissipative structure of SPRDSS using panel data collected from 30 Chinese provinces (excluding Tibet, Hong Kong, Macao, and Taiwan) from 2015 to 2019. The results show that the SPRDSS in China has pre-conditions to form a dissipative structure. At present, the SPRDSSs in most Chinese provinces have not yet formed the dissipative structure, but they are gradually evolving into it. The global orderliness of the sharing system is greater in eastern China than in central China and greater in central China than in western China. The potential for improving global orderliness is greater in western China than in central China and is greater in central China than in eastern China. Therefore, proper policies and measures should be adopted to accelerate the construction of SPRDSS based on the evolution of dissipative structure and to promote the sustainable development of the digital sharing economy.

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“…Computer simulations were also reported 13 confirming the occurrence of patterning behaviours in the instability domain of the model; the drawback that locally some component's concentration becomes negative during such evolution could be put right numerically by resetting negative values equal to zero when they appear. Satisfactory, stable patterns are then finally obtained under those conditions (for a mathematical analysis of the drawbacks exhibited by the early models of Turing, see [67,68]).…”

Section: Dissipative Structures (1967)mentioning

confidence: 99%

The rehabilitation of irreversible processes and dissipative structures’ 50th anniversary

Lefever¹

2018

Phil. Trans. R. Soc. A.

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In 2017, Ilya Prigogine would have been 100 years of age. As for any human being, this centenary is a notable event. For him, as a scientist, 2017 was also above all the 50th anniversary of It was indeed in 1967 that for the first time he used this denomination at the occasion of an important scientific event and in publications. The attribution of this qualification for self-organized behaviours of matter only possible far from equilibrium coincided with the outcome of a research effort of more than 25 years. Centred in thermodynamics and statistical physics on the role played by irreversible processes in the physical evolution of matter, the aim of this research is clear from the outset of his scientific career. With visionary personal intuition and iron-willed determination, it was pursued. The road to success had been long and sinuous, but finally it led to what he called the The progresses that stand out as major landmarks of this endeavour that imposed a U-turn with respect to conceptions of classical physics deeply rooted since the nineteenth century will be described. This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (Part 1)'.

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Early models of chemical oscillations failed to provide bounded solutions

Cited by 7 publications

References 35 publications

Unbounded solutions of models for glycolysis

Unbounded solutions of models for glycolysis

An empirical analysis of social public resources digital sharing system: Dissipative structure theory

The rehabilitation of irreversible processes and dissipative structures’ 50th anniversary

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