Isostable reduction of periodic orbits

Abstract

The well-established method of phase reduction neglects information about a limit-cycle oscillator's approach towards its periodic orbit. Consequently, phase reduction suffers in practicality unless the magnitude of the Floquet multipliers of the underlying limit cycle are small in magnitude. By defining isostable coordinates of a periodic orbit, we present an augmentation to classical phase reduction which obviates this restriction on the Floquet multipliers. This framework allows for the study and understanding of periodic dynamics for which standard phase reduction alone is inadequate. Most notably, isostable reduction allows for a convenient and self-contained characterization of the dynamics near unstable periodic orbits.