Abstract:
:A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to phase models, with a single variable describing the phase of the oscillation with respect to some reference state. An analog to phase reduction has recently been proposed for systems with a stable fixed point, and phase reduction for periodic orbits has recently been extended to take into account transverse directions and higher-order terms. This tutorial gives a unified treatment of such phase reduction techniques and illustrates their use through mathematical and biological examples. It also covers the use of phase reduction for designing control algorithms which optimally change properties of the system, such as the phase of the oscillation. The control techniques are illustrated for example neural and cardiac systems.
journal_name
Biol Cybernjournal_title
Biological cyberneticsauthors
Monga B,Wilson D,Matchen T,Moehlis Jdoi
10.1007/s00422-018-0780-zsubject
Has Abstractpub_date
2019-04-01 00:00:00pages
11-46issue
1-2eissn
0340-1200issn
1432-0770pii
10.1007/s00422-018-0780-zjournal_volume
113pub_type
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