Chimera states in time-varying complex networks

TL;DR

This paper explores how time-varying connectivity in coupled oscillator networks can support various stable and dynamic chimera states, revealing new behaviors influenced by the rate of network changes and fluctuations.

Contribution

It introduces a model of time-varying networks of Kuramoto oscillators and demonstrates the existence of stable, breathing, and alternating chimera states under these conditions.

Findings

Stable, breathing, and alternating chimera states can exist in time-varying networks.

Fast connectivity changes allow a low-dimensional description of the system.

Fluctuations induce the onset of alternating chimera states.

Abstract

Chimera states have been recently found in a variety of different coupling schemes and geometries. In most cases, the underlying coupling structure is considered to be static, while many realistic systems display significant temporal changes in the pattern of connectivity. In this work, we investigate a time-varying network made of two coupled populations of Kuramoto oscillators, where the links between the two groups are considered to vary over time. As a main result, we find that the network may support stable, breathing and alternating chimera states. We also find that, when the rate of connectivity changes is fast, compared to the oscillator dynamics, the network may be described by a low-dimensional system of equations. Unlike in the static heterogeneous case, the onset of alternating chimera states is due to the presence of fluctuations, which may be induced either by the finite size of the network or by large switching times.