2007/07/10 by Gil Benkö, Henrik Jeldtoft Jensen, Benkö, Gil +1
Computer Science · Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech #math.DS
paper · pdf · doi:10.48550/arxiv.0707.1439
10 pages, 7 figures
arxiv created 2007/07/10 · openalex publication_date 2007/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.