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Issue 26, 2011
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Stern–Brocot trees in the periodicity of mixed-mode oscillations

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Abstract

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.

Graphical abstract: Stern–Brocot trees in the periodicity of mixed-mode oscillations

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Article information


Submitted
03 Dec 2010
Accepted
13 Jan 2011
First published
21 Feb 2011

Phys. Chem. Chem. Phys., 2011,13, 12191-12198
Article type
Paper

Stern–Brocot trees in the periodicity of mixed-mode oscillations

J. G. Freire and J. A. C. Gallas, Phys. Chem. Chem. Phys., 2011, 13, 12191
DOI: 10.1039/C0CP02776F

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