# Collective dynamics of globally delay-coupled complex Ginzburg-Landau oscillators

## TL;DR

This paper explores how time-delayed coupling influences the collective dynamics of globally coupled complex Ginzburg-Landau oscillators, revealing significant changes in stability, existence domains, and transitions among various collective states.

## Contribution

It provides a comprehensive numerical and analytical study of the effects of time delay on diverse collective states in GCCGL oscillators, highlighting new stability and existence domain shifts.

## Key findings

- Time delay lowers the threshold for collective states.
- Delay shifts the existence domain towards more negative dispersion values.
- Time delay significantly alters the stability of various states.

## Abstract

The effect of time-delayed coupling on the collective behavior of a population of globally coupled complex Ginzburg-Landau (GCCGL) oscillators is investigated. A detailed numerical study is carried out to study the impact of time delay on various collective states that include synchronous states, multicluster states, chaos, amplitude mediated chimeras and incoherent states. It is found that time delay can bring about significant changes in the dynamical properties of these states including their regions of existence and stability. In general, an increase in time delay is seen to lower the threshold value of the coupling strength for the occurrence of such states and to shift the existence domain towards more negative values of the linear dispersion parameter. Further insights into the numerical findings are provided, wherever possible, by exact equilibrium and stability analysis of these states in the presence of time delay.