# Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105

## TL;DR

This paper develops Lyapunov functions for a non-linear FitzHugh-Nagumo model to analyze the stability and bursting behavior of the microquasar GRS 1915+105's X-ray emissions.

## Contribution

It introduces a biparametric family of Lyapunov functions for the model, enabling stability analysis and understanding of bursting phenomena.

## Key findings

- Demonstrates a theorem on global stability.
- Analyzes transition between bursting and stable states.
- Provides tools to investigate equilibrium properties.

## Abstract

This paper introduces a biparametric family of Lyapunov functions for a non-linear mathematical model based on the FitzHugh-Nagumo equations able to reproduce some main features of the X-ray bursting behaviour exhibited by the microquasar GRS 1915+105. These functions are useful to investigate the properties of equilibrium points and allow us to demonstrate a theorem on the global stability. The transition between bursting and stable behaviour is also analyzed.