# Control of amplitude chimeras by time delay in dynamical networks

## TL;DR

This paper explores how introducing time delays in the coupling of Stuart-Landau oscillators affects amplitude chimera states, showing that delay can significantly extend or reduce their lifetime and influence the transition to synchronized states.

## Contribution

It demonstrates that different types of coupling delays can be used to control the lifetime and dynamics of amplitude chimeras in oscillator networks.

## Key findings

- Time delay can significantly extend the lifetime of amplitude chimeras.
- Different delay types can be used to control the transition to synchronization.
- Generalized Kuramoto order parameter helps characterize state transitions.

## Abstract

We investigate the influence of time-delayed coupling in a ring network of non-locally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. We focus on amplitude chimeras which exhibit incoherent behavior with respect to the amplitude rather than the phase and are transient patterns, and show that their lifetime can be significantly enhanced by coupling delay. To characterize their transition to phase-lag synchronization (coherent traveling waves) and other coherent structures, we generalize the Kuramoto order parameter. Contrasting the results for instantaneous coupling with those for constant coupling delay, for time-varying delay, and for distributed-delay coupling, we demonstrate that the lifetime of amplitude chimera states and related partially incoherent states can be controlled, i.e., deliberately reduced or increased, depending upon the type of coupling delay.