Journal ArticleDOI
Bifurcation of periodic orbits in a chemical reaction problem
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TLDR
In this article, the Hopf-Friedrichs bifurcation theory is applied to the chemical reaction problem and the stability of periodic orbits is obtained by algebraic means.Abstract:
The bifurcation and stability of periodic orbits is obtained by algebraic means for a chemical reaction problem that has been extensively studied recently. After a summary of the Hopf-Friedrichs bifurcation theory, the application to the chemical reaction problem is given to demonstrate the technique and the type of information that is obtainable from this theory.read more
Citations
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On the dynamics of distillation processes—I: The simple distillation of multicomponent non-reacting, homogeneous liquid mixtures
TL;DR: In this article, the mathematical theory of multicomponent simple distillation processes is presented and it is shown that every azeotropic point and pure component vertex corresponds to a singular point and that both elementary and non-elementary singular points may arise.
Journal ArticleDOI
Multiplicity, stability, and oscillatory dynamics of the tubular reactor
TL;DR: In this paper, the authors present numerical procedures for computing the Hopf bifurcation formulas which can determine the stability and location of the oscillation without integrating the parabolic partial differential equations.
Journal ArticleDOI
Smallest chemical reaction system with Hopf bifurcation
Thomas Wilhelm,Reinhart Heinrich +1 more
TL;DR: In this article, the smallest at most bimolecular chemical reaction system with Hopf bifurcation is presented, and a more extensive proof that this system is really the searched smallest one is given.
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Time delay in prey-predator models— II. Bifurcation theory
TL;DR: In this article, the authors studied the Hopf bifurcation in the Volterra model and showed that there is a stable periodic solution in the small, but for parameters such that a long time delay is required to make the equilibrium point locally unstable there is no such stable solution.
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Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks
A. I. Mees,P. E. Rapp +1 more
TL;DR: It is found that oscillations are possible even if both Hill coefficients are equal to one and a numerical method can be used to find periodic solutions and determine their stability by locating a zero of the displacement map.
References
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Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Journal ArticleDOI
Chemical instabilities and sustained oscillations.
René Lefever,Grégoire Nicolis +1 more
TL;DR: The temporal behaviour of a chemical system beyond a non-equilibrium unstable transition is analysed and compared to the behaviour of Volterra-Lotka type systems and certain types of biological rythmic phenomena are discussed.