Oscillations in networks of networks stem from adaptive nodes with memory

TL;DR

This paper develops an analytical framework to study how adaptive nodes with memory influence oscillations in complex networks, revealing how network parameters affect oscillation frequency and modes.

Contribution

It introduces a novel analytical approach to understand oscillations in networks of adaptive, memory-enabled nodes, including networks of networks with diverse cluster modes.

Findings

Oscillation frequency increases with node excitability and network degree.

Oscillation frequency decreases with delays between nodes.

Diverse cluster oscillation modes depend on network topology.

Abstract

We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response failures. The frequency of the oscillations was quantitatively found to increase with the excitability of the nodes and with the average degree of the network and to decrease with delays between nodes. For networks of networks, diverse cluster oscillation modes were found as a function of the topology. Analytical results are in agreement with large-scale simulations and open the horizon for understanding network dynamics composed of finite memory nodes as well as their different phases of activity.