Journal
PHYSICS LETTERS A
Volume 375, Issue 7, Pages 1097-1103Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2011.01.017
Keywords
Mixed-mode oscillations; Stern-Brocot tree; Farey tree; Period-adding; Periodicity hub; Phase diagram
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Funding
- FCT, Portugal [SFRH/BPD/43608/2008]
- CNPq, Brazil
- Air Force Office of Scientific Research [FA9550-07-1-0102]
- Fundação para a Ciência e a Tecnologia [SFRH/BPD/43608/2008] Funding Source: FCT
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We report a systematic two-parameter study of the organization of mixed-mode oscillations and period-adding sequences observed in an extended Bonhoeffer-van der Pol and in a FitzHugh-Nagumo oscillator. For both systems, we construct isospike diagrams and show that the number of spikes of their periodic oscillations are organized in a remarkable hierarchical way, forming a Stern-Brocot tree. The Stern-Brocot tree is more general than the Farey tree. We conjecture the Stern-Brocot tree to also underlie the hierarchical structure of periodic oscillations of other systems supporting mixed-mode oscillations. (C) 2011 Elsevier B.V. All rights reserved.
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