Using a phase space cross section to study large complex systems

Gil Benkö; Henrik Jeldtoft Jensen

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arXiv · 0707.1439

Using a phase space cross section to study large complex systems

Gil Benkö·Henrik Jeldtoft Jensen

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Abstract

For large coupled nonlinear systems, it is difficult to visualize the high-dimensional phase space, which has been thoroughly studied in smaller systems with regards to phenomena such as riddled basins. Here we propose a method to reduce the phase space by defining a phase space cross section. The method is applied to a system of dynamically coupled maps introduced by Ito & Kaneko (Phys. Rev. Lett., 88, 028701, 2001 & Phys. Rev. E, 67, 046226, 2003). We show that the transitions between phases of different synchronization behaviour are not always sharp but can be characterized by fractal boundaries in both phase and parameter space.

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Gil Benkö, Henrik Jeldtoft Jensen. 2007-07-10. Using a phase space cross section to study large complex systems. https://arxiv.org/abs/0707.1439

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