Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems, 2nd Edition

Topic Information

Dear Colleagues,

The need for dynamics and control of nonlinear oscillating systems is ubiquitous in engineering given that real-world engineering systems are, in general, nonlinear and oscillatory.

This multidisciplinary field encompasses computation, physics, mathematics, electrical and mechanical engineering, chemical processes, and so forth.

The objective of this topic is to propose a set of publications providing a forum for discussing and disseminating the latest approaches, methodologies, results, and current challenges in nonlinear dynamics and chaotic systems.

Contributions that focus on all analytical, computational, and experimental aspects of nonlinear dynamics, chaos, and control, including fractional approaches, electromechanical systems at MACRO, MEMS, and NEMS scales, nonideal oscillating systems (limited power supplies), and novel phenomena and behaviors linked to several aspects of symmetry on nonlinear dynamics, chaos, and control, are welcome.

This theme will also be a great opportunity for disseminating recent developments in analytical and numerical techniques and for discussing novel phenomena and behaviors involving several aspects of nonlinear dynamics and control. In addition, works related to relevant and current issues, such as epidemiological models, rumor dissemination, and complex systems are also welcome.

Lastly, researchers and practitioners are invited to submit their original research work in the rapidly developing field of nonlinear dynamics and control of system oscillations and their applications to engineering and science. Therefore, we encourage the submission of researchers’ and practitioners’ latest unpublished works.

Prof. Dr. Jose Balthazar
Prof. Dr. Angelo Marcelo Tusset
Prof. Dr. Átila Madureira Bueno
Dr. Diego Colón
Dr. Marcus Varanis
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Sciences applsci	2.5	5.5	2011	16 Days	CHF 2400	Submit
Axioms axioms	1.6	-	2012	21.7 Days	CHF 2400	Submit
Dynamics dynamics	0.9	1.7	2021	18.2 Days	CHF 1200	Submit
Machines machines	2.5	4.7	2013	17.6 Days	CHF 2400	Submit
Mathematics mathematics	2.2	4.6	2013	17.3 Days	CHF 2600	Submit
Symmetry symmetry	2.2	5.3	2009	15.8 Days	CHF 2400	Submit

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Published Papers (4 papers)

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All Axioms Dynamics Mathematics Symmetry Machines Applied Sciences

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19 pages, 24535 KB  

Open AccessArticle

Synchronization of Bursting Pulse-Coupled Neurons in a Simulation Modeling Environment

by Mikhail Mishchenko, Daniil Chindarev, Vyacheslav Rybin, Valerii Ostrovskii, Yulia Bobrova and Ekaterina Kopets

Mathematics 2026, 14(9), 1430; https://doi.org/10.3390/math14091430 - 24 Apr 2026

Viewed by 397

Abstract

Bursting is a special dynamic mode of neurons that consists of several consecutive spikes separated by a period of quiescence. This paper considers the synchronization of two non-identical neurons capable of both spiking and bursting behavior connected by a unidirectional pulse coupling. Unlike [...] Read more.

Bursting is a special dynamic mode of neurons that consists of several consecutive spikes separated by a period of quiescence. This paper considers the synchronization of two non-identical neurons capable of both spiking and bursting behavior connected by a unidirectional pulse coupling. Unlike most studies, which focus on purely mathematical modeling and numerical simulations, we use simulation modeling of a neuron based on a phase-locked loop (PLL) in addition to the conventional solving of ODEs. Using these two approaches, we demonstrate the fundamental possibility of synchronizing two neurons operating in different dynamic modes. Synchronization regions are constructed in the system parameter space. It is shown that synchronization is achieved both for two spiking neurons and for neurons generating bursting activity. The results obtained are of interest from either a fundamental perspective, as an example of a complex nonlinear system with rich dynamic behavior, or from an applied perspective. In particular, the proposed model can be used in the field of neuromorphic electronics, where not only biological plausibility is important but also the possibility of simple hardware implementation. Differences between the simulation model and the results of numerical solution of ODEs are also demonstrated, revealing the importance of proper simulation frameworks at different design levels of neuromorphic electronics. Full article

(This article belongs to the Topic Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems, 2nd Edition)

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27 pages, 10874 KB  

Open AccessArticle

Experimental Study on the Non-Smooth Behavior of Cage-Less Ball Bearings with Localized Functional Grooves

by Jingwei Zhang, Enwen Zhou, Yibo Wang, Qiyin Lv and Yuan Zhang

Machines 2026, 14(4), 419; https://doi.org/10.3390/machines14040419 - 9 Apr 2026

Viewed by 262

Abstract

To investigate the non-smooth behaviour of cage-less ball bearings with localised functional grooves, this article first designs temperature-varying comparative experiments and rolling element discrete performance test protocols. Subsequently, it analyses the principles of heat generation, transmission, and exchange within ball bearings, establishing a [...] Read more.

To investigate the non-smooth behaviour of cage-less ball bearings with localised functional grooves, this article first designs temperature-varying comparative experiments and rolling element discrete performance test protocols. Subsequently, it analyses the principles of heat generation, transmission, and exchange within ball bearings, establishing a mathematical model for bearing thermal displacement using a dynamic model. This is followed by an analysis of rolling element discrete conditions. Finally, based on experimental results, a comparative analysis of ball bearing temperature variations under combined multi-variable loading conditions is conducted. By altering radial load, axial load, and rotational speed to measure bearing friction torque under different operating conditions, the suitability of bearing operating conditions is analysed, evaluated, and optimised. Full article

(This article belongs to the Topic Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems, 2nd Edition)

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18 pages, 653 KB  

Open AccessReview

Chaos in Control Systems: A Review of Suppression and Induction Strategies with Industrial Applications

by Asad Shafique, Georgii Kolev, Oleg Bayazitov, Yulia Bobrova and Ekaterina Kopets

Mathematics 2025, 13(24), 4015; https://doi.org/10.3390/math13244015 - 17 Dec 2025

Viewed by 1442

Abstract

In control systems, chaos is a natural dualistic phenomenon that can be both a beneficial resource to be used and a negative phenomenon to be avoided. The study examines two opposing paradigms: positive chaotic control, which aims to enhance performance, and negative chaos [...] Read more.

In control systems, chaos is a natural dualistic phenomenon that can be both a beneficial resource to be used and a negative phenomenon to be avoided. The study examines two opposing paradigms: positive chaotic control, which aims to enhance performance, and negative chaos management, which aims to stabilize a system. More sophisticated suppression methods, including adaptive neural networks, sliding mode control, and model predictive control, can decrease convergence times. Controlled chaotic dynamics have significantly impacted the domain of embedded control systems. Specialized controller designs include fractal-based systems and hybrid switching systems that offer better control of chaotic behavior in many situations. The paper highlights the key issues that are related to chaos-based systems, such as the need to implement them in real time, parameter sensitivity, and safety. Recent research suggests an increased interdependence between artificial intelligence, quantum computing, and sustainable technology. The synthesis shows that chaos control has evolved into an engineering field, significantly impacting the industry, which was initially a theoretical concept. It also offers exclusive ideas in the design and improvement of complex control systems. Full article

(This article belongs to the Topic Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems, 2nd Edition)

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15 pages, 717 KB  

Open AccessArticle

A Combined Separation of Variables and Fractional Power Series Approach for Selected Boundary Value Problems

by Gabriel Antonio Felipe, Carlos Alberto Valentim and Sergio Adriani David

Dynamics 2025, 5(3), 24; https://doi.org/10.3390/dynamics5030024 - 20 Jun 2025

Cited by 1 | Viewed by 947

Abstract

Fractional modeling has emerged as an important resource for describing complex phenomena and systems exhibiting non-local behavior or memory effects, finding increasing application in several areas in physics and engineering. This study presents the analytical derivation of equations pertinent to the modeling of [...] Read more.

Fractional modeling has emerged as an important resource for describing complex phenomena and systems exhibiting non-local behavior or memory effects, finding increasing application in several areas in physics and engineering. This study presents the analytical derivation of equations pertinent to the modeling of different systems, with a focus on heat conduction. Two specific boundary value problems are addressed: a Helmholtz equation modified with a fractional derivative term, and a fractional formulation of the Laplace equation applied to steady-state heat conduction in circular geometry. The methodology combines the separation of variables technique with fractional power series expansions, primarily utilizing the Caputo fractional derivative. An important aspect of this paper is its instructional emphasis, wherein the mathematical derivations are presented with detail and clarity. This didactic approach is intended to make the analytical methodology transparent and more understandable, thereby facilitating greater comprehension of the application of these established methods to non-integer-order systems. The final goal is not only to provide a different approach of solving these physical models analytically, but to provide a clear, guided pathway for those engaging in the treatment of fractional differential equations. Full article

(This article belongs to the Topic Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems, 2nd Edition)

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