# Center Manifold and Lie Symmetry Calculations on a Quasi-chemical Model for Growth-death Kinetics in Food

## TL;DR

This paper applies dynamical systems and Lie symmetry methods to analyze a bacterial growth-death model in food, providing insights into its mathematical structure and validating results against existing food science models.

## Contribution

It introduces a novel application of center manifold and Lie symmetry calculations to a food microbiology model, enhancing understanding of its dynamics.

## Key findings

- Calculation of center manifolds for the model
- Identification of Lie symmetries under various parameters
- Comparison with existing food science results

## Abstract

Food scientists at the U.S. Army's Natick Solider Center have developed a model for the lifecyle of the bacteria Staphylococcus aureus in intermediate moisture bread. In this article, we study this model using dynamical systems and Lie symmetry methods. We calculate center manifolds and Lie symmetries for different cases of parameter values and compare our results to those of the food scientists.