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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: 15 May 2026 | Viewed by 1555

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

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Keywords

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

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Published Papers (2 papers)

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Research

40 pages, 12246 KB  
Article
Nonlinear Stochastic Dynamics of the Intermediate Dispersive Velocity Equation with Soliton Stability and Chaos
by Samad Wali, Maham Munawar, Atef Abdelkader, Adil Jhangeer and Mudassar Imran
Entropy 2025, 27(11), 1176; https://doi.org/10.3390/e27111176 - 20 Nov 2025
Viewed by 375
Abstract
This paper examines the nonlinear behavior of the generalized stochastic intermediate dispersive velocity (SIdV) equation, which has been widely analyzed in a non-noise deterministic framework but has yet to be studied in any depth in the presence of varying forcing strength and noise [...] Read more.
This paper examines the nonlinear behavior of the generalized stochastic intermediate dispersive velocity (SIdV) equation, which has been widely analyzed in a non-noise deterministic framework but has yet to be studied in any depth in the presence of varying forcing strength and noise types, in particular how it switches between periodic, quasi-periodic, and chaotic regimes. A stochastic wave transformation reduces the equation to simpler ordinary differential equations to make soliton overlap analysis feasible to analyze soliton robustness under deterministic and stochastic conditions. Lyapunov exponents, power spectra, recurrence quantification, correlation dimension, entropy measures, return maps, and basin stability are then used to measure the effect of white, Brownian, and colored noise on attractor formation, system stability, and spectral correlations. Order–chaos transitions as well as noise-induced complexity are more effectively described by bifurcation diagrams and by Lyapunov spectra. The results of this experiment improve the theoretical knowledge of stochastic nonlinear waves and offer information that will be useful in the fields of control engineering, energy harvesting, optical communications, and signal processing applications. Full article
(This article belongs to the Special Issue Nonlinear Dynamics of Complex Systems)
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10 pages, 2312 KB  
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
Cited by 1 | Viewed by 709
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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