title: Stern-Brocot trees in the periodicity of mixed-mode oscillations.
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.
authors.affiliation: Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil.
authors.forename: Joana G
authors.initials: JG
authors.lastname: Freire
authors.forename: Jason A C
authors.initials: JA
authors.lastname: Gallas