# Chimera states in complex networks: interplay of fractal topology and delay

## TL;DR

This paper investigates how fractal network topology and time delay influence the emergence and control of chimera states, revealing parameter regions where these patterns can be stabilized or suppressed.

## Contribution

It introduces the analysis of chimera states in hierarchical networks of Van der Pol oscillators with delay, showing how delay can be used to control pattern stability.

## Key findings

- Chimera states exist in tongue-like regions in parameter space.
- Time delay can stabilize or destabilize chimera states.
- Delay allows deliberate control of spatio-temporal patterns.

## Abstract

Chimera states are an example of intriguing partial synchronization patterns emerging in networks of identical oscillators. They consist of spatially coexisting domains of coherent (synchronized) and incoherent (desynchronized) dynamics. We analyze chimera states in networks of Van der Pol oscillators with hierarchical connectivities, and elaborate the role of time delay introduced in the coupling term. In the parameter plane of coupling strength and delay time we find tongue-like regions of existence of chimera states alternating with regions of existence of coherent travelling waves. We demonstrate that by varying the time delay one can deliberately stabilize desired spatio-temporal patterns in the system.