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Symmetry
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Symmetry in Nonlinear Dynamics
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Symmetry in Nonlinear Dynamics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1162

Special Issue Editors

Dr. Chaoran Liu

E-Mail Website
Guest Editor
Department of Mechanics, Beijing University of Technology, Beijing 100124, China
Interests: nonlinear dynamics; vibration control; energy harvesting
Special Issues, Collections and Topics in MDPI journals
Dr. Shitong Fang

E-Mail Website
Guest Editor
College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China
Interests: smart materials and structures; energy harvesting; simultaneous vibration suppression and energy harvesting; nonlinear dynamics and control
Special Issues, Collections and Topics in MDPI journals
Dr. Guobiao Hu

E-Mail Website
Guest Editor
Internet of Things Thrust, The Hong Kong University of Science and Technology (Guangzhou), Nansha, Guangzhou 511400, China
Interests: elastic metamaterials; energy harvesting; vibration suppression; optimization; artificial neural network
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear dynamical phenomena are prevalent in mechanical, civil, aerospace, and other engineering fields, giving rise to complex and intriguing dynamic occurrences, such as bifurcation, chaos, and super-/sub-harmonic resonances. While engineering nonlinear dynamics may lead to unfavorable consequences, they can also occasionally bring about beneficial effects that linear dynamical systems can never achieve. Additionally, there are many symmetry, mathematics theory, and algorithm issues in nonlinear dynamics. Thus, there is a pressing need for extensive research to be carried out regarding symmetry in nonlinear dynamical problems.

Dr. Chaoran Liu
Dr. Shitong Fang
Prof. Dr. Guobiao Hu
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. Symmetry 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 2400 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

  • Nonlinear Dynamics
  • Dynamical System
  • Symmetry

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Published Papers (2 papers)

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Research

41 pages, 1444 KiB  
Article
Symmetries and Closed-Form Solutions for Some Classes of Dynamical Systems
by Remus-Daniel Ene, Nicolina Pop and Rodica Badarau
Symmetry 2025, 17(4), 546; https://doi.org/10.3390/sym17040546 - 3 Apr 2025
Viewed by 222
Abstract
The present paper focuses on some classes of dynamical systems involving Hamilton–Poisson structures, while neglecting their chaotic behaviors. Based on this, the closed-form solutions are obtained. These solutions are derived using the Optimal Auxiliary Functions Method (OAFM). The impact of the physical parameters [...] Read more.
The present paper focuses on some classes of dynamical systems involving Hamilton–Poisson structures, while neglecting their chaotic behaviors. Based on this, the closed-form solutions are obtained. These solutions are derived using the Optimal Auxiliary Functions Method (OAFM). The impact of the physical parameters of the system is also investigated. Periodic orbits around the equilibrium points are performed. There are homoclinic or heteroclinic orbits and they are obtained in exact form. The dynamical system is reduced to a second-order nonlinear differential equation, which is analytically solved through the OAFM procedure. The influence of initial conditions on the system is explored, specifically regarding the presence of symmetries. A good agreement between the analytical and corresponding numerical results is demonstrated, reflecting the accuracy of the proposed method. A comparative analysis underlines the advantages of the OAFM compared with the iterative method. The results of this work encourage the study of dynamical systems with bi-Hamiltonian structure and similar properties as physical and biological problems. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics)
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15 pages, 3893 KiB  
Article
Correlative Dynamics of Complex Systems: A Multifractal Perspective of Motion Based on SL(2R) Symmetry
by Vlad Ghizdovat, Emanuel Nazaretian, Catalin Gabriel Dumitras, Maricel Agop, Constantin Placinta, Calin Buzea, Cristina Marcela Rusu, Decebal Vasincu and Zoltan Borsos
Symmetry 2025, 17(1), 27; https://doi.org/10.3390/sym17010027 - 27 Dec 2024
Viewed by 506
Abstract
By assimilating any complex system into a multifractal, a new approach for describing the dynamics of such systems is proposed by means of the Multifractal Theory of Motion. In such context, the description of these dynamics is accomplished through continuous and non-differentiable curves [...] Read more.
By assimilating any complex system into a multifractal, a new approach for describing the dynamics of such systems is proposed by means of the Multifractal Theory of Motion. In such context, the description of these dynamics is accomplished through continuous and non-differentiable curves (multifractal curves), giving rise to two scenarios. The first scenario is a Schrödinger-type multifractal scenario, a situation in which the motion laws can be related to the SL(2R) algebra invariant functions. The second scenario is a Madelung-type multifractal scenario, a situation in which if the differentiable and non-differentiable components of the velocity field satisfy a particular restriction, an SL(2R) symmetry can also be highlighted. Moreover, correlative dynamics in either of the two scenarios, based on the same SL(2R) symmetry, can be obtained by Riccati-type gauges, which imply Stoler coherent states. Several cases induced by the SL(2R) symmetry are also analyzed. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics)
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