Geometric decomposition of planar vector fields with a limit cycle

TL;DR

This paper introduces a numerical algorithm for analyzing the geometric structure of planar dynamical systems exhibiting limit cycles, bridging the gap between abstract models and biological applications.

Contribution

It presents a novel algorithm for the geometric decomposition of planar vector fields with limit cycles, enhancing analysis of biological dynamical systems.

Findings

Algorithm successfully computes geometric structures of systems with limit cycles.

Provides a new tool for studying biological phenomena modeled by planar systems.

Bridges the gap between theoretical analysis and experimental modeling in biology.

Abstract

Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key features but remain disconnected from experimental manipulation. Geometric methods have been useful in connecting both approaches, although they have only been established for specific type of systems. Phenomena of biological relevance, such as limit cycles, are still difficult to study using conventional methods. In this paper, I explore an alternative description of planar dynamical systems and I present an algorithm to compute numerically the geometric structure of planar systems with a limit cycle.