# A new method to reduce the number of time delays in a network

## TL;DR

This paper introduces a numerical method to further reduce the number of time delays in coupled dynamical networks, improving upon existing theoretical bounds while preserving the network's dynamic behavior.

## Contribution

It presents a new formulation and numerical approach to minimize time delays in networks beyond the theoretical lower bound, enhancing control and analysis.

## Key findings

- Numerical solutions can beat the theoretical lower bound for delay reduction.
- The proposed method effectively minimizes delays while maintaining network dynamics.
- The approach offers practical benefits for designing and controlling complex networks.

## Abstract

Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can behave unexpectedly when the signal between the vertices are time delayed. It has been shown for a very general class of systems that the time delays can be rearranged as long as the total time delay over the constitutive loops of the network is conserved. This fact allows to reduce the number of time delays of the problem without loss of information. There is a theoretical lower bound for this number, but in many cases we can find a numerical solution that beats this limit. Here we propose a formulation of the problem and a numerical method to even further reduce the number of time delays in a network.