# Delay engineered solitary states in complex networks

## TL;DR

This paper introduces a method to create and control solitary states in complex networks of oscillators by strategically adding delays to specific links, enabling precise manipulation of partial synchronization patterns.

## Contribution

The study demonstrates how delayed links can be used to engineer and control solitary states in neural and chaotic oscillator networks, a novel approach in network synchronization control.

## Key findings

- Solitary states can be induced by introducing delays in network links.
- The position and extent of solitary nodes are controllable via delay values and locations.
- Delay engineering allows reshaping of solitary state patterns in the network.

## Abstract

We present a technique to engineer solitary states by means of delayed links in a network of neural oscillators and in coupled chaotic maps. Solitary states are intriguing partial synchronization patterns, where a synchronized cluster coexists with solitary nodes displaced from this cluster and distributed randomly over the network. We induce solitary states in the originally synchronized network of identical nodes by introducing delays in the links for a certain number of selected network elements. It is shown that the extent of displacement and the position of solitary elements can be completely controlled by the choice (values) and positions (locations) of the incorporated delays, reshaping the delay engineered solitary states in the network.