Symmetry in Chaotic Systems and Circuits III

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 2263

Special Issue Editor


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Guest Editor
Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece
Interests: electrical and electronics engineering; mathematical modeling; control theory; engineering, applied and computational mathematics; numerical analysis; mathematical analysis; numerical modeling; modeling and simulation; robotics
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Special Issue Information

Dear Colleagues,

Chaos theory is one of the most fascinating fields in modern science, revolutionizing our understanding of order and pattern in nature. Symmetry, a traditional and highly developed area of mathematics, would seem to lie at the opposite end of the spectrum. However, in the last few years, scientists have found connections between these two areas, connections that can have profound consequences for our understanding of the complex behavior in many physical, chemical, biological, and mechanical chaotic systems.

Therefore, symmetry can play an important role in the field of nonlinear systems and especially in the field of designing nonlinear circuits that produce chaos. More specifically, from designing chaotic systems and circuits with symmetric nonlinear terms to the study of a system’s equilibria with symmetry in the case of self-excited attractors or symmetric line of equilibria in the case of hidden attractors, the feature of symmetry can play a significant role in such systems.

The aim of this Special Issue is to collect contributions considering nonlinear chaotic systems and circuits that present any of the aforementioned symmetries. Applications of chaotic systems and circuits where symmetry—or the deliberate lack of symmetry—is present are also welcome.

Dr. Christos Volos
Guest Editor

Manuscript Submission Information

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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

  • chaos
  • nonlinear systems
  • nonlinear circuits
  • control
  • synchronization
  • symmetric nonlinearities
  • self-excited attractors
  • hidden attractors
  • applications of chaotic systems and circuits with symmetries

Published Papers (2 papers)

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Research

14 pages, 313 KiB  
Article
Stabilization of Nonlinear Systems with External Disturbances Using the DE-Based Control Method
by Keran Sun, Xiaolong Wang and Rongwei Guo
Symmetry 2023, 15(5), 987; https://doi.org/10.3390/sym15050987 - 26 Apr 2023
Cited by 3 | Viewed by 817
Abstract
This paper investigates the stabilization of nonlinear systems with external disturbances, which are both bounded and unbounded. Firstly, the stabilization problem of the nominal nonlinear system is realized, and the corresponding stabilization controllers are designed. Then, three suitable filters are proposed and applied [...] Read more.
This paper investigates the stabilization of nonlinear systems with external disturbances, which are both bounded and unbounded. Firstly, the stabilization problem of the nominal nonlinear system is realized, and the corresponding stabilization controllers are designed. Then, three suitable filters are proposed and applied to asymptotically estimate the corresponding disturbances, and the disturbance estimators are presented and used to exactly eliminate the corresponding disturbances. Then, the disturbance estimator (DE)-based controllers are proposed to stabilize such nonlinear systems. It should be pointed out the unbounded disturbances are exactly estimated by suitable filters, which has advantages over the existing results. Finally, two illustrative examples, which have certain symmetrical properties, are taken, and the related numerical simulations are carried out to verify the effectiveness and correctness of the proposed results. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits III)
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10 pages, 5462 KiB  
Article
Influence of Parametric Symmetry on the Dynamics of 3D Sinusoidal Discrete Systems
by Karthikeyan Rajagopal, Sathiyadevi Kanagaraj, Christos Volos and Anitha Karthikeyan
Symmetry 2023, 15(4), 780; https://doi.org/10.3390/sym15040780 - 23 Mar 2023
Cited by 1 | Viewed by 894
Abstract
The discrete system serves an important role in mimicking collective dynamics found in continuous dynamical systems, which are relevant to many realistic natural and artificial systems. To investigate the dynamical transition of a discrete system, we employ three-dimensional sinusoidal discrete maps with an [...] Read more.
The discrete system serves an important role in mimicking collective dynamics found in continuous dynamical systems, which are relevant to many realistic natural and artificial systems. To investigate the dynamical transition of a discrete system, we employ three-dimensional sinusoidal discrete maps with an additional self feedback factor. Specifically, we focus on dynamical transitions with respect to the bifurcation parameter, sine function amplitude, and intensity of self feedback factors. We demonstrate the presence of symmetry in relation to parametric variation using two parameter diagrams. The study is then expanded to the network of sine maps in the presence of self-feedback factor. We discover that negative feedback exhibits the transition from cluster state to synchronization while raising the coupling strength for small-world network interactions. Furthermore, increasing feedback from negative to positive causes the transition from synchronization to desynchronization via chimera state for various complex network connectivities. Full article
(This article belongs to the Special Issue Symmetry in Chaotic Systems and Circuits III)
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