# Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks

## TL;DR

This paper compares symbolic and numerical methods for identifying parameter regions with multiple steady states in biological networks, demonstrating the effectiveness of a new graph-theoretical symbolic preprocessing technique.

## Contribution

The paper introduces a novel graph-theoretical symbolic preprocessing method that enhances the efficiency of symbolic computation in biological network analysis.

## Key findings

- Symbolic methods outperform numerical ones after preprocessing.
- Preprocessing significantly reduces computation time.
- Enhanced accuracy in identifying multistationarity regions.

## Abstract

We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing.