Paper Info
Title
Weakly Connected Quasi-periodic Oscillators, FM Interactions, and Multiplexing in the Brain
Abstract
We prove that weakly connected networks of quasi-periodic (multifrequency) oscillators can be transformed into a phase model by a continuous change of variables. The phase model has the same form as the one for periodic oscillators with the exception that each phase variable is a vector. When the oscillators have mutually nonresonant frequency (rotation) vectors, the phase model uncouples. This implies that such oscillators do not interact even though there might be physical connections between them. When the frequency vectors have mutual low-order resonances, the oscillators interact via phase deviations. This mechanism resembles that of the FM radio, with a shared feature-multiplexing of signals. Possible applications to neuroscience are discussed.
Year
DOI
Venue
1999
10.1137/S0036139997330623
SIAM JOURNAL ON APPLIED MATHEMATICS
Keywords
Field
DocType
weakly connected neural networks,invariant manifolds,quasi-periodic oscillators,chaos,phase model,resonances,FM interactions,multiplexing,oscillatory neurocomputer,thalamocortical system
Change of variables,Topology,Oscillation,Mathematical analysis,Control theory,Synchronization networks,Multiplexing,Periodic graph (geometry),Resonance,Mathematics
Journal
Volume
Issue
ISSN
59
6
0036-1399
Citations 
PageRank 
References 
5
1.82
5
Authors
1
Name
Order
Citations
PageRank
Eugene M. Izhikevich11340166.74