Exploring Parameter Spaces in Dynamical Systems
Abstract
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on parameters. Using a classical problem from mathematical ecology as an example, we demonstrate how to apply the algorithm to investigate the amplitude of a limit cycle depending on seven parameters. We stress the practical value of the algorithm but we also provide a rigorous error analysis to justify the overall strategy. Our approach turns out to be particularly useful in the case of comparing experimental data to a model defined by differential equations and to investigate whether the equations can approximate the modeled system.
Cite
@article{arxiv.0807.1993,
title = {Exploring Parameter Spaces in Dynamical Systems},
author = {Christian Kuehn},
journal= {arXiv preprint arXiv:0807.1993},
year = {2008}
}