Dynamics in a phase model of half-center oscillator: two neurons with excitatory coupling

TL;DR

This paper introduces a minimalistic phase model of two excitatory neurons forming a half-center oscillator, analyzing their dynamic states and bifurcations to understand rhythmic activity in biological systems.

Contribution

It presents a new simplified model capturing key dynamics of half-center oscillators, including bifurcation analysis of different rhythmic states.

Findings

Identified parameter regions for in-phase, anti-phase, and quiescent states.

Analyzed bifurcation transitions between different dynamic regimes.

Model serves as a foundational component for studying rhythmic neural activity.

Abstract

A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of dynamics, characteristic for central pattern generators: respectively, in-phase, anti-phase synchronous oscillations and quiescence, and study various bifurcation transitions between all these states. Suggested model can serve as a building block of specific complex central pattern generators for studies of rhythmic activity and information processing in animals and humans.