Chapter 1 - Mechanisms of Phase-Locking and Frequency Control in Pairs of Coupled Neural Oscillators*

This chapter discusses the mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. The behavioral repertoire of two-component networks includes synchronized oscillations, anti-phase oscillations, phase-locked oscillations with phase difference other than zero or π,as well as non-phase-locked solutions and steady states. It is not possible to analyze the general behavior of a pair of coupled nonlinear oscillators. However, if the coupling is sufficiently weak, then it is possible to reduce the behavior of a general coupled system to something much simpler. The full system can be reduced to a single equation for the difference in the phases of the oscillators. The special structure of neural equations and the kinds of coupling between them translates into constraints on the reduced equations that can be used to understand the circumstances under which the oscillators synchronize or stabilize at other phase differences. Furthermore, it is possible to build networks with flexible synchronization properties by taking advantage of the variation in behavior in different voltage regimes.