In this work we study a system of Kuramoto oscillators with identical frequencies in a Cayley tree. Heterogeneity in the frequency distribution is introduced in the root of the tree, allowing for analytical calculations of the phases evolution.

A prediction scheme for spatio-temporal time series is presented that is based on reconstructed local states. As a numerical example the ev olution of a Kuramoto-Siv ashinsky equation is forecasted using previously sampled data.

We present asymptotic relaxation estimates to bi-cluster configurations for the ensemble of Kuramoto oscillators with two different natural frequencies which have been observed in numerical simulations. We provide a set of initial configurations with a positive Lebesgue measure in T leading to bi-(point) cluster configurations consisting of linear combinations of two Dirac measures in super-thr...

Abstract Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based a recent formulation weighted simplicial complexes phases supported simplices any order k , we introduce linear and non-linear frustration terms independent orientation + 1 s...

Robert Adler, best known as the co-inventor of the television remote control, died in February at the age of 93. He had been active, as a consultant in ultrasonics, well beyond the age of 90. Indeed, the last of his approximately 180 U.S. patents is dated February 1, 2007—two weeks before his death. Adler was born in Vienna in 1913 and received a doctorate in physics from the University of Vien...