# Global bifurcation map of the homogeneus states in the Gray-Scott model

## TL;DR

This paper provides a comprehensive bifurcation map of homogeneous states in the Gray-Scott model, identifying key bifurcations and their global organization through rigorous and numerical methods.

## Contribution

It offers the first detailed global bifurcation map of the Gray-Scott model's homogeneous states, combining rigorous verification and numerical continuation.

## Key findings

- Identification of Takens Bogdanov bifurcations
- Detection of Bautin bifurcations
- Global bifurcation structure mapped in parameter space

## Abstract

We study the spatially homogeneous time dependent solutions and their bifurcations of the Gray-Scott model. We find the global map of bifurcations by a combination of rigorous verification of the existence of Takens Bogdanov and a Bautin bifurcations, in the space of two parameters k and F. With the aid of numerical continuation of local bifurcation curves we give a global description of all the possible bifurcations