The Structure of Instantaneous Phase Resetting in a Neural Oscillator

Abstract

In order to ultimately gain an understanding of the central pattern generators (CPG) involved in rhythmic motor activity such as locomotion and respiration it is necessary to understand the phase resetting behavior of the neural oscillators that comprise such circuits. In this study, we ignore action potential generation and instead focus on the underlying oscillations whose plateaus comprise the bursts and whose troughs comprise the interburst hyperpolarizations. We have examined the structure of phase resetting in neural oscillators. As an illustrative example, we will use Morris-Lecar oscillator, which, despite its simplicity, reproduces with sufficient accuracy the membrane potential envelope of a neural oscillator. The qualitative characterization of a limit cycle oscillator as a phase oscillator, a relaxation oscillator, or an intermediate determines the relationship between time elapsed (temporal phase) and distance traversed along the limit cycle (geometric phase). A mapping between geometric phase and temporal phase was found to provide insight into the shape of the phase resetting curve (PRC).