Differentiability implies continuity in neuronal dynamics

Citation
Jt. Francis et al., Differentiability implies continuity in neuronal dynamics, PHYSICA D, 148(1-2), 2001, pp. 175-181
Citations number
31
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
PHYSICA D
ISSN journal
0167-2789 → ACNP
Volume
148
Issue
1-2
Year of publication
2001
Pages
175 - 181
Database
ISI
SICI code
0167-2789(20010101)148:1-2<175:DICIND>2.0.ZU;2-R
Abstract
Recent work has identified nonlinear deterministic structure in neuronal dy namics using periodic orbit theory. Troublesome in this work were the signi ficant periods of time where no periodic orbits were extracted - ''dynamica lly dark" regions. Tests for periodic orbit structure typically require tha t the underlying dynamics are differentiable. Since continuity of a mathema tical function is a necessary but insufficient condition for differentiabil ity, regions of observed differentiability should be fully contained within regions of continuity. We here verify that this fundamental mathematical p rinciple is reflected in observations from mammalian neuronal activity. Fir st, we introduce a null Jacobian transformation to verify the observation o f differentiable dynamics when periodic orbits are extracted. Second, we sh ow that a less restrictive test for deterministic structure requiring only continuity demonstrates widespread nonlinear deterministic structure only p artially appreciated with previous approaches. (C) 2001 Published by Elsevi er Science B.V.