Optimal waveform for the entrainment of a weakly forced oscillator.
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.
Harada
Takahiro
T
Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan.
Tanaka
Hisa-Aki
HA
Hankins
Michael J
MJ
Kiss
István Z
IZ
D008956:Models, Chemical; D009532:Nickel / Q000737:chemistry; D013464:Sulfuric Acids / Q000737:chemistry
D013464:Sulfuric Acids; D009532:Nickel; C033158:sulfuric acid