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