University of Oulu

Kühnlenz F, Nardelli PHJ (2016) Dynamics of Complex Systems Built as Coupled Physical, Communication and Decision Layers. PLoS ONE 11(1): e0145135.

Dynamics of complex systems built as coupled physical, communication and decision layers

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Author: Kuhnlenz, Florian1; Nardelli, Pedro H. J.1
Organizations: 1Univ Oulu, Dept Commun Engn, FI-90014 Oulu, Finland.
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 2.2 MB)
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Language: English
Published: Public Library of Science, 2016
Publish Date: 2021-07-12


This paper proposes a simple model to capture the complexity of multilayer systems where their constituent layers affect, and are affected by, each other. The physical layer is a circuit composed by a power source and resistors in parallel. Every individual agent aims at maximizing its own delivered power by adding, removing or keeping the resistors it has; the delivered power is in turn a non-linear function that depends on the other agents’ behavior, its own internal state, its global state perception, the information received from its neighbors via the communication network and a randomized selfishness. We develop an agent-based simulation to analyze the effects of number of agents (system size), communication network topology, communication errors and the minimum power gain that triggers a behavioral change on the system dynamic. Our results show that a wave-like behavior at macro-level (caused by individual changes in the decision layer) can only emerge for a specific system size. The ratio between cooperators and defectors depends on the minimum gain assumed-lower minimal gains lead to less cooperation, and vice-versa. Different communication network topologies imply different levels of power utilization and fairness at the physical layer, and a certain level of error in the communication layer induces more cooperation.

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Series: PLoS one
ISSN: 1932-6203
ISSN-E: 1932-6203
ISSN-L: 1932-6203
Volume: 11
Issue: 1
Article number: e0145135
DOI: 10.1371/journal.pone.0145135
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
Funding: Funding support was provided by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (BR)[312146/2012-4] (; the Academy of Finland (; the joint funded project A Theory for Sustainable Smart Grids: Combining Communication Theory, Power Systems, Signal Processing and Economics from a Complexity Science Perspective (SUSTAIN), which covers the authors' salary costs, and the Strategic Research Council/Finnish Academy BC-DC project (n.292854). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Academy of Finland Grant Number: 292854
Detailed Information: 292854 (Academy of Finland Funding decision)
Dataset Reference: This research was carried out using different open-source Python ( tools including: NumPy (, IPython (, NetworkX ( and Matplotlib ( The code used to perform the simulation scenarios can be found under
Copyright information: © 2016 Kühnlenz, Nardelli. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited