# Quantitative modeling and analysis of bifurcation-induced bursting

## TL;DR

This paper introduces a novel method for modeling neuronal dynamics that leverages time scale separation and bifurcation analysis to achieve both qualitative and quantitative solution features.

## Contribution

It presents a new approach for guiding model development and parameter tuning using slow-fast variable dynamics and bifurcation landscapes.

## Key findings

- Method effectively captures qualitative behaviors of neuronal models.
- Enables quantitative matching of solution features through designed slow variable dynamics.
- Provides a framework for model simplification and parameter estimation in complex systems.

## Abstract

Modeling and parameter estimation for neuronal dynamics are often challenging because many parameters can range over orders of magnitude and are difficult to measure experimentally. Moreover, selecting a suitable model complexity requires a sufficient understanding of the model's potential use, such as highlighting essential mechanisms underlying qualitative behavior or precisely quantifying realistic dynamics. We present a novel approach that can guide model development and tuning to achieve desired qualitative and quantitative solution properties. Our approach relies on the presence of disparate time scales and employs techniques of separating the dynamics of fast and slow variables, which are well known in the analysis of qualitative solution features. We build on these methods to show how it is also possible to obtain quantitative solution features by imposing designed dynamics for the slow variables in the form of specified two-dimensional paths in a bifurcation-parameter landscape.