Volume 100, Number 4, November 2012
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||04 December 2012|
Stern-Brocot trees in spiking and bursting of sigmoidal maps
Institute for Multiscale Simulations, Friedrich-Alexander-Universität - 91052 Erlangen, Germany, EU and Departamento de Física, Universidade Federal da Paraíba - 58051-970 João Pessoa, Brazil
Received: 10 October 2012
Accepted: 30 October 2012
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.
PACS: 89.75.Fb – Structures and organization in complex systems / 89.75.Kd – Patterns
© EPLA, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.