Complexities

16 pages, 932 KB

Open AccessArticle

A Duplication–Divergence Hypergraph Model for Protein Complex Data

by Ruihua Zhang and Gesine Reinert

Complexities 2025, 1(1), 7; https://doi.org/10.3390/complexities1010007 - 3 Dec 2025

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Hypergraphs, a generalisation of traditional graphs in which hyperedges may connect more than two vertices, provide a natural framework for modeling higher-order interactions in complex biological systems. In the context of protein complexes, hypergraphs capture relationships in which a single protein may participate [...] Read more.

Hypergraphs, a generalisation of traditional graphs in which hyperedges may connect more than two vertices, provide a natural framework for modeling higher-order interactions in complex biological systems. In the context of protein complexes, hypergraphs capture relationships in which a single protein may participate in multiple complexes simultaneously. A fundamental question is how such protein complex hypergraphs evolve over time. Motivated by duplication–divergence–deletion models often used for protein–protein interaction networks, we propose a novel Duplication–Divergence Hypergraph (DDH) model for the evolutionary dynamics of protein complex hypergraphs. To evaluate network resilience, we simulate targeted attack strategies analogous to drug treatments or genetic knockouts that remove selected proteins and their associated hyperedges. We measure the resulting structural changes using hypergraph-based efficiency metrics, comparing synthetic networks generated by the DDH model with empirical E. coli protein complex data. This framework demonstrates closer alignment with empirical observations than standard pairwise duplication–divergence models, suggesting that hypergraphs provide a more realistic representation of protein interactions. Full article

(This article belongs to the Special Issue Modeling Complex Interactions Beyond Networks)

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16 pages, 793 KB

Open AccessReview

The Concept of Homeodynamics in Systems Theory

by Hugues Petitjean, Serge Finck, Patrick Schmoll and Alexandre Charlet

Complexities 2025, 1(1), 6; https://doi.org/10.3390/complexities1010006 - 27 Nov 2025

Cited by 2 | Viewed by 1857

Abstract

This review traces the historical evolution, conceptual foundations, and contemporary applications of the term homeodynamics across biological, ecological, cognitive, and social systems. Initially coined in the 19th century but largely forgotten, the term re-emerged in the second half of the 20th century as [...] Read more.

This review traces the historical evolution, conceptual foundations, and contemporary applications of the term homeodynamics across biological, ecological, cognitive, and social systems. Initially coined in the 19th century but largely forgotten, the term re-emerged in the second half of the 20th century as scholars sought to describe dynamic stability in open, self-organizing systems. From Yates’s theoretical formalization in biology to Rattan’s work in biogerontology and recent applications in psychology and organizational theory, homeodynamics has progressively evolved from a synonym of homeostasis to a distinct systems concept. It now denotes the capacity of complex systems to sustain coherence through transitions between multiple temporary equilibria, integrating feedbacks, bifurcations, and adaptive reconfigurations. By revisiting the term’s lineage, this review clarifies its epistemological scope and proposes its use as a heuristic and modeling framework for understanding dynamic stability and regime shifts in living and social systems. Full article

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16 pages, 1097 KB

Open AccessArticle

Forecasting Chaotic Dynamics Using a Hybrid System

by Michele Baia, Franco Bagnoli and Tommaso Matteuzzi

Complexities 2025, 1(1), 5; https://doi.org/10.3390/complexities1010005 - 20 Nov 2025

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Abstract

The literature is rich with studies and examples on parameter estimation obtained by analyzing the evolution of chaotic dynamical systems, even when only partial information is available through observations. However, parameter estimation alone does not resolve prediction challenges, particularly when only a subset [...] Read more.

The literature is rich with studies and examples on parameter estimation obtained by analyzing the evolution of chaotic dynamical systems, even when only partial information is available through observations. However, parameter estimation alone does not resolve prediction challenges, particularly when only a subset of variables is known or when parameters are estimated with a significant uncertainty. In this paper, we introduce a hybrid system specifically designed to address this issue. Our method involves training an artificial intelligence system to predict the dynamics of a measured system by combining a neural network with a simulated system. By training the neural network, it becomes possible to refine the model’s predictions so that the simulated dynamics synchronizes with that of the system under investigation. After a brief contextualization of the problem, we introduce the hybrid approach employed, describing the learning technique and testing the results on three chaotic systems inspired by atmospheric dynamics in measurement contexts. Although these systems are low-dimensional, they encompass all the fundamental characteristics and predictability challenges that can be observed in more complex real-world systems. Full article

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15 pages, 6979 KB

Open AccessArticle

Extended Gauss Iterative Map: Bistability and Chimera States

by Derik W. Gryczak, Ervin K. Lenzi and Antonio M. Batista

Complexities 2025, 1(1), 4; https://doi.org/10.3390/complexities1010004 - 13 Nov 2025

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Abstract

We investigate an extended Gauss iterative map by incorporating the q-exponential function, a key component of the Tsallis framework. This extension enables us to investigate the non-linear dynamics of the Gauss iterative map across a broader range of scenarios, encompassing periodic, chaotic, [...] Read more.

We investigate an extended Gauss iterative map by incorporating the q-exponential function, a key component of the Tsallis framework. This extension enables us to investigate the non-linear dynamics of the Gauss iterative map across a broader range of scenarios, encompassing periodic, chaotic, and bistable behaviors. Regular and chaotic phenomena have been observed in coupled systems. In this context, we propose a network of coupled extended Gauss iterative maps. In our network, we found the emergence of chimera states, characterized by the coexistence of coherent and incoherent behaviors. These states are identified within specific parameter regimes using Gopal’s metric. In this work, we show the interplay between chaos and emergent collective dynamics in coupled extended Gauss iterative maps. Full article

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14 pages, 2615 KB

Open AccessArticle

A Particle-Based Model of Endothelial Cell Dynamics in the Extracellular Matrix

by Kazuma Sakai, Tatsuya Hayashi, Jun Mada and Tetsuji Tokihiro

Complexities 2025, 1(1), 3; https://doi.org/10.3390/complexities1010003 - 11 Nov 2025

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Abstract

Branching structures such as vascular networks are representative morphological patterns in living systems, and they often arise from collective cell migration. Angiogenesis, the sprouting of new blood vessels from pre-existing ones, is a fundamental process in development. Experimental and theoretical studies have demonstrated [...] Read more.

Branching structures such as vascular networks are representative morphological patterns in living systems, and they often arise from collective cell migration. Angiogenesis, the sprouting of new blood vessels from pre-existing ones, is a fundamental process in development. Experimental and theoretical studies have demonstrated that sprout formation depends on the collective movements and shapes of endothelial cells, as well as the remodelling of the extracellular matrix. Many discrete models have been proposed to describe cell dynamics, successfully reproducing vascular patterns and collective behaviours. In this study, we present a two-dimensional mathematical model that represents each endothelial cell as an ellipse and incorporates the effects of the extracellular matrix. We performed computer simulations under two scenarios: invasion from a pre-formed sprout and collective advancement into an extracellular matrix region. The results show that the extracellular matrix helps maintain linear sprout extension and suppresses the formation of dispersed or curved branches, while elongated cell shapes promote sprouting more effectively than round cells. The model also reproduces experimentally observed behaviours such as tip-cell replacement and the mixing of cells within sprouts. These findings highlight the importance of integrating cell shape and extracellular matrix remodelling to understand early blood vessel formation. Full article

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18 pages, 17130 KB

Open AccessReview

A Simple Overview of Complex Systems and Complexity Measures

by Luiz H. A. Monteiro

Complexities 2025, 1(1), 2; https://doi.org/10.3390/complexities1010002 - 11 Jun 2025

Cited by 2 | Viewed by 6428

Abstract

Defining a complex system and evaluating its complexity typically requires an interdisciplinary approach, integrating information theory, signal processing techniques, principles of dynamical systems, algorithm length analysis, and network science. This overview presents the main characteristics of complex systems and outlines several metrics commonly [...] Read more.

Defining a complex system and evaluating its complexity typically requires an interdisciplinary approach, integrating information theory, signal processing techniques, principles of dynamical systems, algorithm length analysis, and network science. This overview presents the main characteristics of complex systems and outlines several metrics commonly used to quantify their complexity. Simple examples are provided to illustrate the key concepts. Speculative ideas regarding these topics are also discussed here. Full article

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2 pages, 303 KB

Open AccessEditorial

Complexities: An Open Access Journal for the Field of Complex Systems

by José F. F. Mendes

Complexities 2025, 1(1), 1; https://doi.org/10.3390/complexities1010001 - 27 Feb 2025

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Abstract

On behalf of the MDPI Editorial Board and Staff, I am pleased to announce the launch of Complexities (ISSN: 3042-6448) [...] Full article

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Complexities, Volume 1, Issue 1 (December 2025) – 7 articles

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