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Updated: Jun 8, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
Published on: June 29, 2018
Optimal waveform for the entrainment of a weakly forced oscillator
Takahiro Harada1, Hisa-Aki Tanaka, Michael J Hankins
1Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan.
Abstract:
A theory for obtaining a waveform for the effective entrainment of a weakly forced oscillator is presented. Phase model analysis is combined with calculus of variation to derive a waveform with which entrainment of an oscillator is achieved with a minimum power forcing signal. Optimal waveforms are calculated from the phase response curve and a solution to a balancing condition. The theory is tested in chemical entrainment experiments in which oscillations close to and farther away from a Hopf bifurcation exhibited sinusoidal and higher harmonic nontrivial optimal waveforms, respectively.
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