Synchronous Propagation of Periodic Signals in Feedforward Networks of Standard Model Neurons

TL;DR

This paper investigates how periodic signals propagate synchronously in feedforward neural networks, establishing stability conditions and demonstrating that various neuron models can maintain stable signal transmission.

Contribution

It extends the theory of periodic signal propagation to standard neuron models, providing stability criteria and numerical evidence for transversely Floquet stable propagation.

Findings

Periodic signals can propagate stably in neural chains.

Stability conditions are applicable across multiple neuron models.

Numerical simulations confirm transversely Floquet stability.

Abstract

Periodic signals propagating along chains are common in biology, for example in locomotion and peristalsis, and are also of interest for continuum robots. In previous work we constructed such networks as 'feedforward lifts' of a central pattern generator (CPG). When the CPG undergoes periodic oscillations, created by Hopf bifurcation or other mechanisms, it can then transmit periodic signals along one or more feedforward chains in a synchronous or phase-synchronous manner. We proved necessary and sufficient conditions for the stability of these lifted periodic orbits, in several senses. Here we examine the implications of the resulting theory for chains of neurons, using several standard neuron models: FitzHugh-Nagumo, Morris-Lecar, Hindmarsh-Rose, and Hodgkin-Huxley. We compare different notions of transverse stability, and summarize some numerical simulations showing that for all these neuron models the propagating signal can be transversely Floquet stable. Finally we discuss implications for less idealized models.