Journal ArticleDOI
Some further studies of nonlinear oscillations in chemical systems
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TLDR
In this paper, the behavior of a single chemical oscillator coupled in series illustrates the phenomena of synchronization, multiply periodic and almost-periodic oscillations, and subharmonic resonance.Abstract:
That chemical reactions can exhibit all of the interesting and well known behavior of nonlinear oscillators is shown by collecting the scattered results in the literature for a simple reaction mechanism, supplementing them with some new results, and analyzing the behavior of the single chemical oscillator using the method of isoclines. Furthermore, two oscillators coupled in series illustrate the phenomena of synchronization, multiply periodic and almost‐periodic oscillations, and subharmonic resonance. Finally the reaction mechanism is modified to a form which is biochemically realistic and still behaves similarly to the original scheme.read more
Citations
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Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction
TL;DR: In this paper, the authors generalized the chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction by a model composed of five steps involving three independent chemical intermediates.
Journal ArticleDOI
Classification of biological networks by their qualitative dynamics.
TL;DR: Techniques are given to classify biological networks into classes having similar qualitative dynamics, illustrated by considering dynamic data from a number of biological systems and showing how the deep structure of each system can be determined.
Journal ArticleDOI
On the stability of coupled chemical oscillators
TL;DR: In this paper, the stable steady states obtained by coupling two, three and more Brusselators in parallel, in a diffusion-like manner, are discussed, and the symmetry patterns of the stable domains are analyzed.
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Numerical Approximations of Stochastic Differential Equations With Non-globally Lipschitz Continuous Coefficients
TL;DR: In this article, moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method were established.
References
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Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Journal ArticleDOI
The Chemical Basis of Morphogenesis
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.