Journal
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
Volume 13, Issue 26, Pages 12191-12198Publisher
ROYAL SOC CHEMISTRY
DOI: 10.1039/c0cp02776f
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Funding
- FCT, Portugal [SFRH/BPD/43608/2008]
- CNPq, Brazil
- US Air Force Office of Scientific Research [FA9550-07-1-0102]
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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.
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