Solitary states in adaptive nonlocal oscillator networks

TL;DR

This paper investigates a nonlocal ring network of adaptively coupled phase oscillators, revealing various synchronized states, analyzing their stability, and uncovering how solitary states emerge due to adaptivity.

Contribution

It provides the first detailed stability analysis of rotating waves and explains the emergence of solitary states through bifurcation scenarios in adaptive networks.

Findings

Stability of rotating waves depends on coupling structure and wavenumber.

Solitary states emerge due to adaptivity and are classified by bifurcation scenarios.

Multiple frequency-synchronized states, including phase-locked and multicluster, are observed.

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.