Using a phase space cross section to study large complex systems
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2007
- DOI:
- 10.48550/arXiv.0707.1439
- arXiv:
- arXiv:0707.1439
- Bibcode:
- 2007arXiv0707.1439B
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- Mathematics - Dynamical Systems
- E-Print:
- 10 pages, 7 figures