2011/08/16 by Paulo F. C. Tilles, Tilles, Paulo F. C., Hilda A. Cerdeira +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Environmental Science · #Adaptation and Self-Organizing Systems (nlin.AO) #Ecosystem dynamics and resilience #Evolution and Genetic Dynamics #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1108.3271
openalex publication_date 2011/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we study the local coupled Kuramoto model with periodic boundary\nconditions. Our main objective is to show how analytical solutions may be\nobtained from symmetry assumptions, and while we proceed on our endeavor we\nshow apart from the existence of local attractors, some unexpected features\nresulting from the symmetry properties, such as intermittent and chaotic period\nphase slips, degeneracy of stable solutions and double bifurcation composition.\nAs a result of our analysis, we show that stable fixed points in the\nsynchronized region may be obtained with just a small amount of the existent\nsolutions, and for a class of natural frequencies configuration we show\nanalytical expressions for the critical synchronization coupling as a function\nof the number of oscillators, both exact and asymptotic.\n