# Dynamics of slow and fast systems on complex networks

## TL;DR

This paper investigates how mixed slow and fast dynamical systems on complex networks exhibit various synchronized states, amplitude death, and a transition from fast to slow collective behavior as the number of slow systems increases.

## Contribution

It introduces the study of frequency synchronization and amplitude death in networks with mixed time scales, analyzing transitions and motifs of minimal configurations.

## Key findings

- Identification of frequency synchronized states with tunable frequencies
- Observation of amplitude death and multifrequency states
- Crossover from fast to slow collective dynamics as slow systems increase

## Abstract

We study the occurrence of frequency synchronised states with tunable emergent frequencies in a network of connected systems. This is achieved by the interplay between time scales of nonlinear dynamical systems connected to form a network, where out of N systems, m evolve on a slower time scale. In such systems, in addition to frequency synchronised states, we also observe amplitude death, synchronised clusters and multifrequency states. We report an interesting cross over behaviour from fast to slow collective dynamics as the number of slow systems m increases. The transition to amplitude death is analysed in detail for minimal network configurations of 3 and 4 systems which actually form possible motifs of the full network.