Special Issue "Symmetry in Modeling and Analysis of Dynamic Systems"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics and Symmetry/Asymmetry".

Deadline for manuscript submissions: closed (5 January 2022) | Viewed by 7520

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Special Issue Editor

Special Issue Information

Dear Colleagues,

The proposed Special Issue (SI) of the journal Symmetry aims to cover the exchange and dissemination of the concept of symmetry in the modelling and analysis of dynamic features occurring in various branches of science including physics, chemistry, biology, and engineering (mechanics, mechatronics, civil engineering, electronics, informatics, bioengineering, etc.).

The approaches based on dynamical symmetry breaking generalize and unify theories developed and employed in the aforementioned sciences under the concept of invariance of the global/local behavior of the points of spacetime, including temporal/spatiotemporal symmetries.

Since a property of the symmetry of the investigated system implies its conservation quantity like energy, linear/angular momentum, electric charge etc., contributions of research based on the mathematical models of nonlinear partial and ordinary differential equations are especially welcome.

The following topics are also included: (i) discrete vs. continuous symmetry breaking; (ii) solitary waves; (iii) symmetry breaking instability; (iv) symmetry exhibited by MEMS/NEMS; (v) arrays of oscillators subjected to electric/magnetic/thermal fields; (vi) time-symmetry breaking in quantum oscillators; (vii) symmetry breaking of resonances; (viii) symmetry in fluid-structure interaction; (ix) symmetry vs. asymmetry in pattern formation; (x) symmetry in solid-gas phase transition; (xi) continuous vs. discontinuous symmetry; (xii) temporal vs. spatiotemporal symmetry; (xiii) symmetry in transition from regular to chaotic dynamics.

Prof. Jan Awrejcewicz
Guest Editor

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 1800 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 ODES and PDEs
  • stability
  • bifurcation
  • chaos
  • resonance
  • boundary conditions

Published Papers (9 papers)

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Research

Article
Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator
Symmetry 2021, 13(7), 1207; https://doi.org/10.3390/sym13071207 - 05 Jul 2021
Cited by 1 | Viewed by 527
Abstract
In this paper, we consider a perturbed partial discrete Dirichlet problem with the (p,q)-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the [...] Read more.
In this paper, we consider a perturbed partial discrete Dirichlet problem with the (p,q)-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the origin on the nonlinear term f, we obtain the sufficient conditions for the existence of infinitely many small solutions. As far as we know, this is the study of perturbed partial discrete boundary value problems. Finally, the results are exemplified by an example. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
Article
Vibration Properties of a Concrete Structure with Symmetries Used in Civil Engineering
Symmetry 2021, 13(4), 656; https://doi.org/10.3390/sym13040656 - 12 Apr 2021
Cited by 3 | Viewed by 943
Abstract
The paper aims to study a concrete structure, currently used in civil engineering, which has certain symmetries. This type of problem is common in engineering practice, especially in civil engineering. There are many reasons why structures with identical elements or certain symmetries are [...] Read more.
The paper aims to study a concrete structure, currently used in civil engineering, which has certain symmetries. This type of problem is common in engineering practice, especially in civil engineering. There are many reasons why structures with identical elements or certain symmetries are used in industry, related to economic considerations, shortening the design time, for constructive, simplicity, cost or logistical reasons. There are many reasons why the presence of symmetries has benefits for designers, builders, and beneficiaries. In the end, the result of these benefits materializes through short execution times and reduced costs. The paper studies the eigenvalue and eigenmode properties of vibration for components of the constructions’ structure, often encountered in current practice. The identification of such properties allows the simplification and easing of the effort necessary for the dynamic analysis of such a structure. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
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Article
Evaluating the Impact of Different Symmetrical Models of Ambient Assisted Living Systems
Symmetry 2021, 13(3), 450; https://doi.org/10.3390/sym13030450 - 10 Mar 2021
Cited by 9 | Viewed by 876
Abstract
In recent years, numerous attempts have been made to enhance the living standard for old-aged people. Ambient Assisted Living (AAL) is an evolving interdisciplinary field aimed at the exploitation of knowledge and communication technology in health and tele-monitoring systems to combat the impact [...] Read more.
In recent years, numerous attempts have been made to enhance the living standard for old-aged people. Ambient Assisted Living (AAL) is an evolving interdisciplinary field aimed at the exploitation of knowledge and communication technology in health and tele-monitoring systems to combat the impact of the growing aging population. AAL systems are designed for customized, responsive, and predictive requirements, requiring high performance of functionality to ensure interoperability, accessibility, security, and consistency. Standardization, continuity, and assistance of system development have become an urgent necessity to meet the increasing needs for sustainable systems. In this article, we examine and address the methods of the different AAL systems. In addition, we analyzed the acceptance criteria of the AAL framework intending to define and evaluate different AAL-based symmetrical models, leveraging performance characteristics under the integrated fuzzy environment. The main goal is to provide an understanding of the current situation of the AAL-oriented setups. Our vision is to investigate and evaluate the potential symmetrical models of AAL systems and frameworks for the implementation of effective new installations. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
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Article
Dynamical Simulation of Effective Stem Cell Transplantation for Modulation of Microglia Responses in Stroke Treatment
Symmetry 2021, 13(3), 404; https://doi.org/10.3390/sym13030404 - 02 Mar 2021
Cited by 1 | Viewed by 637
Abstract
Stem cell transplantation therapy may inhibit inflammation during stroke and increase the presence of healthy cells in the brain. The novelty of this work, is to introduce a new mathematical model of stem cells transplanted to treat stroke. This manuscript studies the stability [...] Read more.
Stem cell transplantation therapy may inhibit inflammation during stroke and increase the presence of healthy cells in the brain. The novelty of this work, is to introduce a new mathematical model of stem cells transplanted to treat stroke. This manuscript studies the stability of the mathematical model by using the current biological information on stem cell therapy as a possible treatment for inflammation from microglia during stroke. The model is proposed to represent the dynamics of various immune brain cells (resting microglia, pro-inflammation microglia, and anti-inflammation microglia), brain tissue damage and stem cells transplanted. This model is based on a set of five ordinary differential equations and explores the beneficial effects of stem cells transplanted at early stages of inflammation during stroke. The Runge–Kutta method is used to discuss the model analytically and solve it numerically. The results of our simulations are qualitatively consistent with those observed in experiments in vivo, suggesting that the transplanted stem cells could contribute to the increase in the rate of ant-inflammatory microglia and decrease the damage from pro-inflammatory microglia. It is found from the analysis and simulation results that stem cell transplantation can help stroke patients by modulation of the immune response during a stroke and decrease the damage on the brain. In conclusion, this approach may increase the contributions of stem cells transplanted during inflammation therapy in stroke and help to study various therapeutic strategies for stem cells to reduce stroke damage at the early stages. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
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Article
Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior
Symmetry 2021, 13(2), 318; https://doi.org/10.3390/sym13020318 - 14 Feb 2021
Viewed by 661
Abstract
In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the [...] Read more.
In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
Article
Generalized Attracting Horseshoe in the Rössler Attractor
Symmetry 2021, 13(1), 30; https://doi.org/10.3390/sym13010030 - 27 Dec 2020
Viewed by 680
Abstract
We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations—realizable by a rather simple electronic circuit—capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincaré section yielding the desired map is described, but [...] Read more.
We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations—realizable by a rather simple electronic circuit—capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincaré section yielding the desired map is described, but not pursued due to its complexity, which makes the construction of a circuit realization exceedingly difficult. Instead, the generalized attracting horseshoe and its trapping region is obtained by using a carefully chosen Poincaré map of the Rössler attractor. Novel numerical techniques are employed to iterate the map of the trapping region to approximate the chaotic strange attractor contained in the generalized attracting horseshoe, and an electronic circuit is constructed to produce the map. Several potential applications of the idea of a generalized attracting horseshoe and a physical electronic circuit realization are proposed. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
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Article
Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems
Symmetry 2020, 12(12), 1989; https://doi.org/10.3390/sym12121989 - 02 Dec 2020
Cited by 2 | Viewed by 597
Abstract
This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The [...] Read more.
This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions (u(t),v(t)) is that the solution u(t) is positive, and the other solution v(t) may change sign. Finally, two examples with continuous function f1 being positive and f2 being semipositone are worked out to illustrate the main results. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
Article
Existence of Three Solutions for a Nonlinear Discrete Boundary Value Problem with ϕc-Laplacian
Symmetry 2020, 12(11), 1839; https://doi.org/10.3390/sym12111839 - 06 Nov 2020
Cited by 6 | Viewed by 534
Abstract
In this paper, based on critical point theory, we mainly focus on the multiplicity of nontrivial solutions for a nonlinear discrete Dirichlet boundary value problem involving the mean curvature operator. Without imposing the symmetry or oscillating behavior at infinity on the nonlinear term [...] Read more.
In this paper, based on critical point theory, we mainly focus on the multiplicity of nontrivial solutions for a nonlinear discrete Dirichlet boundary value problem involving the mean curvature operator. Without imposing the symmetry or oscillating behavior at infinity on the nonlinear term f, we respectively obtain the sufficient conditions for the existence of at least three non-trivial solutions and the existence of at least two non-trivial solutions under different assumptions on f. In addition, by using the maximum principle, we also deduce the existence of at least three positive solutions from our conclusion. As far as we know, our results are supplements to some well-known ones. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
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Article
On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations
Symmetry 2020, 12(6), 1033; https://doi.org/10.3390/sym12061033 - 19 Jun 2020
Cited by 2 | Viewed by 1044
Abstract
The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on [...] Read more.
The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on the Taylor’s decomposition method on three and two points. The theorem on the stability of the presented difference scheme is proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations are obtained. Finally, in order to ensure the coincidence between experimental and theoretical results and to clarify how efficient the proposed scheme is, some numerical experiments are tested. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)
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