Determining Parameters Leading to Chaotic Dynamics in Systems

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.