Theoretical Analysis of Phase Resetting on Matsuoka Oscillators

Abstract

In this paper, we consider functional roles of phase resetting of the piecewise linear oscillator model known as the Matsuoka oscillator, which widely applied in the field of robotics, particularly, in the design of central pattern generator (CPG) units for controlling robotic rhythmic motion. The oscillator can be regarded as a fast-slow system composed of a fast membrane potential dynamics and a slow recovery dynamics. Firstly, we show phase response curves (PRCs) for both the dynamics based on the phase reduction approach, and plausibility of phase resetting through the slow dynamics as well as the fast dynamics during periodic motion. Secondly, we show plausibility of feedback inputs to the slow dynamics rather than the fast dynamics by using a singular perturbation approach. Our results will bridge the gap among theoretical analysis, design principle, and practical and efficient implementation for applications in robotics and biomedical engineering.