Entrainment of a Limit-Cycle Oscillator with Shear by Large Amplitude Forcing

Abstract

The entrainment of a circularly symmetric limit-cycle oscillator due to large amplitude periodic forcing is investigated. The unforced oscillator contains parameters controlling the local strength of attraction of the limit cycle and the amount of radial variation of angular velocity, or shear, near the limit cycle. It is shown that entrainment (1:1 phase locking) will occur for sufficiently large amplitude forcing whenever the local strength of attraction to the limit cycle is great enough. Furthermore, if the amount of shear is allowed to increase with the strength of attraction to the limit cycle, then increasing the ratio of shear to strength of attraction can have the effect of increasing the sensitivity of the oscillator to forcing.