Eur. Phys. J. Special Topics 229, 2183–2203 (2020)
https://doi.org/10.1140/epjst/e2020-900253-0

Regular Article

Solitary states in adaptive nonlocal oscillator networks

¹ Institute of Theoretical Physics, TU Berlin, Germany
² Institute of Mathematics, TU Berlin, Germany
³ Department of Physics, Imperial College, London, UK

^a e-mail: rico.berner@physik.tu-berlin.de

Received: 31 October 2019
Accepted: 8 June 2020
Published online: 28 September 2020

Abstract

In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the phase-locked solutions, the rotating waves, we provide a rigorous stability analysis. This analysis shows a strong dependence of their stability on the coupling structure and the wavenumber which is a remarkable difference to an all-to-all coupled network. Despite the fact that solitary states have been observed in a plethora of dynamical systems, the mechanisms behind their emergence were largely unaddressed in the literature. Here, we show how solitary states emerge due to the adaptive feature of the network and classify several bifurcation scenarios in which these states are created and stabilized.