Exploring Parameter Spaces in Dynamical Systems

Details Exploring Parameter Spaces in Dynamical Systems Exploring Parameter Spaces in Dynamical Systems

2008-07-12

arxiv.org/abs/0807.1993v1

Mathematics

Numerical Analysis

Scientific paper

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.

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