Abstract

Analysis of coupled oscillators and their synchronization is commonly performed using first-order phase approximation; the most illustrative example is the celebrated Kuramoto model. In this presentation, we discuss numerical and analytical approaches to high-order reduction and illustrate their usefulness using examples where the first-order model cannot capture the effects. These examples include an explanation of the remote synchronization of indirectly coupled units and a description of a chimera's shape in a ring of non-locally coupled oscillators. Furthermore, we explicitly write the second-order extension of the Kuramoto model.