# Format-Preserving Reduction of Canonical Nonlinear Models

## TL;DR

This paper introduces a method to simplify large biomedical models by replacing differential equations with nullclines, making them easier to analyze and automate.

## Contribution

The novelty lies in a formulaic reduction strategy that preserves the mathematical format of canonical nonlinear models.

## Key findings

- Replacing differential equations with nullclines allows for model simplification while retaining key dynamics.
- The method is particularly effective for canonical S-systems and Lotka–Volterra models.
- The approach is well-suited for automation, enabling optimally reduced model sizes.

## Abstract

The recent upward trend in the size of mathematical models in the biomedical sciences offers novel opportunities and challenges. The latter are partially technical, for instance, in terms of computational efficiency and the need of vastly increased parameter determination, and partly conceptual, as large models make it more difficult to discern which variables are the key drivers of the model dynamics. The article proposes a model size reduction strategy that replaces differential equations with their corresponding nullclines. The result is an approximation whose quality depends on numerous aspects of the analyzed system. In the case of canonical S-systems and Lotka–Volterra models, the proposed reduction is essentially always feasible and retains their mathematical format, thereby facilitating sequential reductions. As these reductions are entirely formulaic, they are ideally suited for automation, which could systematically lead to models of optimally reduced sizes.

The online version contains supplementary material available at 10.1007/s11538-026-01599-2.