2008/07/12 by Christian Kuehn, Kuehn, Christian
Engineering · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.0807.1993
openalex publication_date 2008/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.