Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
5.2
2.2
Journals
Symmetry
Special Issues
Asymmetric and Symmetric Studies on Nonlinear Dynamics
share announcement

Asymmetric and Symmetric Studies on Nonlinear Dynamics

A Special Issue of Symmetry (ISSN 2073-8994) belonging to the section "B: Mathematics".

Deadline for manuscript submissions: 26 May 2027 | Viewed by 1546

Editors

Dr. Subrata Ghosh

E-Mail Website
Guest Editor
Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
Interests: complex networks; dynamical systems
Dr. Ajit Mahata

E-Mail Website
Guest Editor
Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
Interests: time series analysis; econophysics; machine learning in dynamical systems

Special Issue Information

Dear Colleagues,

Symmetries play a significant role in understanding and formulating the foundation of physical laws, with applications ranging from classical physics, mathematics, and dynamical systems. Symmetric systems are those whose governing equations remain invariant under certain transformations, including reflection, rotation, translation, or permutation; equivalently, they are systems that constituted by a homogeneous set of parameters. This invariant often leads to periodic patterns, conserved quantities, and structured behaviors, such as chimera states and cluster synchronization in network systems.

On the other hand, asymmetric systems lack such invariance or heterogeneity, either inherently or due to perturbations. Asymmetry can lead to rich and often unexpected phenomena, including critical transitions, chaos, pattern formation, and synchronization.

The transition from symmetry to asymmetry is particularly important in nonlinear systems for explaining how complex structures and behaviors arise in nature. Studying both symmetric and asymmetric cases provides deeper insight into stability, evolution, and the underlying mechanisms driving nonlinear phenomena across physics, biology, and engineering.

This Special Issue will focus on studies of symmetric and asymmetric systems in nonlinear dynamics, encompassing topics such as stability analysis, collective phenomena, critical transitions, symmetries in networks, the emergence of chaos, and pattern formation.

We look forward to receiving your contributions.

Dr. Subrata Ghosh
Dr. Ajit Mahata
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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
  • mathematical modeling
  • symmetry
  • asymmetry
  • critical transition
  • complex networks

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

18 pages, 324 KB  
Article
Exact Solutions and Periodic Dynamics of a Three-Dimensional Nonlinear Difference System with Delayed Cyclic Interactions
by Yasser Almoteri and Ahmed Ghezal
Symmetry 2026, 18(6), 997; https://doi.org/10.3390/sym18060997 - 10 Jun 2026
Viewed by 313
Abstract
This paper investigates a nonlinear three-dimensional system of difference equations describing the interaction among three mutually dependent sequences evolving over discrete time. The proposed model accounts for nonlinear coupling effects as well as feedback structures that govern the system’s dynamics. We first establish [...] Read more.
This paper investigates a nonlinear three-dimensional system of difference equations describing the interaction among three mutually dependent sequences evolving over discrete time. The proposed model accounts for nonlinear coupling effects as well as feedback structures that govern the system’s dynamics. We first establish the conditions ensuring the well-definedness and solvability of the system, followed by the construction of closed-form expressions of the solutions under appropriate assumptions on the initial data and parameter settings. To support the theoretical findings, numerical experiments are carried out, accompanied by graphical illustrations that reveal the influence of parameter variations on the qualitative dynamics of the system. As an application, we demonstrate how the proposed three-dimensional nonlinear system can be interpreted in the context of delayed cyclic competition among three interacting populations. This application illustrates the relevance of the developed framework to ecological systems exhibiting nonlinear feedback mechanisms and delayed interactions. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Studies on Nonlinear Dynamics)
►▼ Show Figures

Figure 1

24 pages, 1323 KB  
Article
Symmetry-Organised Complexity in Quantum Neural Networks
by Hassan Ugail and Newton Howard
Symmetry 2026, 18(6), 912; https://doi.org/10.3390/sym18060912 - 26 May 2026
Cited by 3 | Viewed by 648
Abstract
Useful quantum neural networks should not merely explore large Hilbert spaces but should organise their expressive capacity according to the symmetries of the learning problem. We introduce symmetry-organised complexity as an ansatz-level, representation-theoretic trajectory diagnostic for quantum neural networks. The diagnostic combines symmetry-sector [...] Read more.
Useful quantum neural networks should not merely explore large Hilbert spaces but should organise their expressive capacity according to the symmetries of the learning problem. We introduce symmetry-organised complexity as an ansatz-level, representation-theoretic trajectory diagnostic for quantum neural networks. The diagnostic combines symmetry-sector organisation, cross-irreducible representation organised complexity, and symmetry metastability into a composite index, which is then multiplied by a compliance factor that penalises apparent complexity arising from symmetry violation. This compliance factor is defined at the level of the implemented trainable generators rather than as a representation-independent channel metric. The representation-theoretic basis of the construction is that, for an exactly equivariant network, the effective trainable operators lie in the commutant of the group action and are controlled by multiplicity dimensions rather than by the full Hilbert-space dimension. We show that joint sector collapse and state freezing force the index to vanish under an explicit multiplicity–purity condition and that networks with identical qubit and parameter counts can have different values of the index. Two analytically tractable four-qubit examples with excitation number and total spin symmetry illustrate how the diagnostic separates sector-collapsed, symmetry-organised, and symmetry-breaking behaviour. A controlled U(1)-compatible teacher–student classification task further shows that, in this validation setting, the ordering of the composite index across equivariant, hybrid, and non-equivariant ansatze agrees with the ordering of generalisation accuracy. The framework is most informative when the relevant symmetry of the learning problem is known. Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Studies on Nonlinear Dynamics)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop