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Nonlinear Dynamics of Complex Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 407

Special Issue Editors


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Guest Editor
Department of Mathematics, “Al. I. Cuza” University of Iasi, 700506 Iasi, Romania
Interests: set-valued measures; non-additive measures; set-valued integrals; non-additive integrals; topology; fractals; multifractals; nonlinear dynamics
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Special Issue Information

Dear Colleagues,

Complex systems consist of a large number of interconnected elements that interact with each other in an adaptive and emergent way. These systems occur in diverse fields, including physics, biology, economics, sociology and computer science. For instance, the main characteristic of a complex system is that its overall properties cannot simply be deduced from the behavior of the individual components, but result from their interactions.

Some key characteristics of complex systems are listed below:

  • Nonlinear interactions;
  • Emergent behavior;
  • Sensitivity to initial conditions;
  • Self-organization;
  • Adaptive dynamics.

In such a context, nonlinear dynamics studies systems in which changes are not proportional to the applied forces, and where interactions can produce unforeseen effects. Many complex systems are governed by nonlinear dynamics, which explains phenomena such as the following:

  • Deterministic Chaos—some complex systems, although governed by deterministic equations, exhibit seemingly random behavior due to sensitivity to initial conditions.
  • Strange attractors—in nonlinear dynamics, a system may have a set of states towards which it naturally tends, but its trajectory is highly complex and unpredictable. This phenomenon explains why some complex systems do not stabilize in a fixed equilibrium, but oscillate in a complicated way.
  • Bifurcations—sudden changes in the behavior of a system when a particular variable crosses a critical threshold.

Taking the above into account, this Special Issue aims at the correspondence between properties of complex systems and nonlinear dynamics. Both theoretical and experimental approaches are considered.

Dr. Alina Cristiana Gavriluţ
Prof. Dr. Maricel Agop
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • deterministic chaos
  • bifurcations
  • strange attractors
  • scale relativity theory
  • multifractality
  • non-linear behavior

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Published Papers (1 paper)

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Research

10 pages, 2312 KiB  
Article
Synchronizations in Complex Systems Dynamics Through a Multifractal Procedure
by Vlad Ghizdovat, Diana Carmen Mirila, Florin Nedeff, Dragos Ioan Rusu, Oana Rusu, Maricel Agop and Decebal Vasincu
Entropy 2025, 27(6), 647; https://doi.org/10.3390/e27060647 - 17 Jun 2025
Viewed by 224
Abstract
The dynamics of complex systems often exhibit multifractal properties, where interactions across different scales influence their evolution. In this study, we apply the Multifractal Theory of Motion within the framework of scale relativity theory to explore synchronization phenomena in complex systems. We demonstrate [...] Read more.
The dynamics of complex systems often exhibit multifractal properties, where interactions across different scales influence their evolution. In this study, we apply the Multifractal Theory of Motion within the framework of scale relativity theory to explore synchronization phenomena in complex systems. We demonstrate that the motion of such systems can be described by multifractal Schrödinger-type equations, offering a new perspective on the interplay between deterministic and stochastic behaviors. Our analysis reveals that synchronization in complex systems emerges from the balance of multifractal acceleration, convection, and dissipation, leading to structured yet highly adaptive behavior across scales. The results highlight the potential of multifractal analysis in predicting and controlling synchronized dynamics in real-world applications. Several applications are also discussed. Full article
(This article belongs to the Special Issue Nonlinear Dynamics of Complex Systems)
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