# The geometry of rest-spike bistability

## TL;DR

This paper introduces an augmented Morris-Lecar model that captures bistability between resting and spiking states, providing a physiologically interpretable and mathematically tractable framework for studying complex neuronal dynamics.

## Contribution

The paper presents a modified Morris-Lecar model with an added slow inward current to accurately model bistability, bridging physiological relevance and mathematical simplicity.

## Key findings

- The augmented model exhibits bistability between resting and spiking states.
- It effectively captures slow spiking and bursting phenomena.
- The model offers a balance of physiological interpretability and analytical tractability.

## Abstract

Morris-Lecar model is arguably the simplest dynamical model that retains both the slow-fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. The resulting dynamical system is a core structure for many dynamical phenomena such as slow spiking and bursting. We show how the proposed model combines physiological interpretation and mathematical tractability and we discuss the benefits of the proposed approach with respect to alternative models in the literature.