Determining Parameters Leading to Chaotic Dynamics in Systems

TL;DR

This paper introduces a computational framework to explore parameter spaces in dynamical systems, helping identify conditions leading to chaos, demonstrated on models of bacterial populations, and visualizing parameter connections without complex math.

Contribution

The paper presents a novel computational approach for analyzing parameter spaces and visualizing chaos-inducing conditions in biological dynamical systems.

Findings

Framework effectively identifies parameters with positive Lyapunov exponents

Visualizations reveal connections between parameters leading to chaos

Applied successfully to bacterial population models

Abstract

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we provide a computational framework which can be used to both explore the parameter space for the existence of positive Lyapunov exponents and visualize the connections between parameters leading to these positive values. We demonstrate the effectiveness of the framework on several dynamical systems used to model bacterial populations with a nutrient source. We provide sample graphics to show the possible ways this framework can be used to gather insight of an underlying system without requiring detailed mathematical analysis.