Stern-Brocot trees in spiking and bursting of sigmoidal maps

Freire JG, Pöschel T, Gallas J (2012)


Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2012

Journal

Publisher: Institute of Physics: EPL

Book Volume: 100

Article Number: 48002

Journal Issue: 4

DOI: 10.1209/0295-5075/100/48002

Abstract

We study the global organization of oscillations in sigmoidal maps, a class of models which reproduces complex locking behaviors commonly observed in lasers, neurons, and other systems which display spiking, bursting, and chaotic sequences of spiking and bursting. We find periodic oscillations to emerge organized regularly according to the elusive Stern-Brocot tree, a symmetric and more general tree which contains the better-known asymmetric Farey tree as a sub-tree. The Stern-Brocot tree provides a natural and encompassing organization to classify nonlinear oscillations. The mathematical algorithm for generating both trees is exactly the same, differing only in the initial conditions. Such degeneracy suggests that the wrong tree might have been attributed to locking phenomena reported in some of the earlier works. © Copyright EPLA, 2012.

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APA:

Freire, J.G., Pöschel, T., & Gallas, J. (2012). Stern-Brocot trees in spiking and bursting of sigmoidal maps. EPL - Europhysics Letters, 100(4). https://dx.doi.org/10.1209/0295-5075/100/48002

MLA:

Freire, J. G., Thorsten Pöschel, and Jason Gallas. "Stern-Brocot trees in spiking and bursting of sigmoidal maps." EPL - Europhysics Letters 100.4 (2012).

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