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The milker-killer dilemma in Utrecht and Tübingen

A report by Thomas Hantke. During his stay at Utrecht University (August 30 - September 4), Johannes Müller (University of Tübingen, financed by NLS) and Thomas Hantke (RIVM Bilthoven, formerly CWI) have been working together on the dynamics of a model-setup of uniformly coupled patches. This model aims to provide a tool to study the `milker-killer dilemma' in a deterministic setting.

While the system of one patch already shows complicated dynamics, they investigated the dynamics of a system of two patches of equal size. They showed that, via a pitchfork bifurcation, the synchronous solution of two patches loses stability and asynchronous solutions appear.

They developed methods to continue the stable and unstable solutions numerically. By identifying parameter ranges for synchronisticallity it is possible to extend conclusions derived analytically for a one-patch system. Numerical experiments show clustering of patches to synchronous solutions. Hereby one can significantly reduce the dimensionality of the system.

As a follow-up of this cooperation, Thomas Hantke visited Johannes Müller in Tübingen in the period of 14-17 September 1998.

Bob Kooi
Thu Oct 1 13:04:44 MET DST 1998