Hybrid Automata and \epsilon-Analysis on a Neural Oscillator

TL;DR

This paper introduces a hybrid automaton model of a neural oscillator, analyzing it with symbolic and approximation methods, including epsilon-semantics, to better understand its behavior and differences from traditional models.

Contribution

It presents a novel hybrid automaton model of a neural oscillator and compares approximation techniques, highlighting the effectiveness of epsilon-semantics in analysis.

Findings

Standard sigmoid-to-step function replacements are inadequate.

Approximation approaches differ significantly in capturing dynamics.

Epsilon-semantics can be practically computed for hybrid models.

Abstract

In this paper we propose a hybrid model of a neural oscillator, obtained by partially discretizing a well-known continuous model. Our construction points out that in this case the standard techniques, based on replacing sigmoids with step functions, is not satisfactory. Then, we study the hybrid model through both symbolic methods and approximation techniques. This last analysis, in particular, allows us to show the differences between the considered approximation approaches. Finally, we focus on approximations via epsilon-semantics, proving how these can be computed in practice.