# Excitable behaviors

arXiv: https://arxiv.org/abs/1704.04989 · HTML: https://mlsanity.com/paper/1704.04989/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2017.

## Built on by (most cited first, 3 of 3)

- [Learning Flow Functions from Data with Applications to Nonlinear Oscillators](https://mlsanity.com/paper/2303.16656/) (2023)
- [A Neuromorphic Architecture for Scalable Event-Based Control](https://mlsanity.com/paper/2511.11924/) (2025)
- [RHYME-XT: A Neural Operator for Spatiotemporal Control Systems](https://mlsanity.com/paper/2603.17867/) (2026)

## Abstract (arXiv)

This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection properties rather than closed systems classified by their parameter ranges. Modeling, analysis, and synthesis questions can be formulated in the classical language of circuit theory. The input-output characterization of excitability is in terms of the local sensitivity of the current-voltage relationship. It suggests the formulation of novel questions for non-linear system theory, inspired by questions from experimental neurophysiology.