Halfway between phase and amplitude oscillators

Antonio Politi
Institute of Pure and Applied Mathematics, University of Aberdeen, UK

Collective properties of oscillators are often analysed by running simulations for increasingly large ensembles of elements. Therefore, analytical approaches/results are definitely welcome as they play the role of references for validating the results on the various scenarios that are otherwise only numerically observed. Here we show that the well known model of mean-field coupled, Stuart-Landau oscillators can be semi- analytically studied at a macroscopic level in an intermediate regime, where the oscillators maintain some typical features of phase-oscillators (remaining aligned along a closed smooth curve), but amplitude oscillations manifest themselves as fluctuations of the curve itself. Our approach allows characterising the collective dynamics for different values of the coupling strengths and in particular to find evidence of self-consistent partial synchrony and an intriguing collective-chaos regime characterised by a small number of positive exponents and a seemingly high-dimensional dynamics.