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Axioms
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Nonlinear Dynamics and Chaos and Their Applications to Engineering and...
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Nonlinear Dynamics and Chaos and Their Applications to Engineering and Science

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 4967

Special Issue Editors

Prof. Dr. José Manoel Balthazar

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Guest Editor
1. Mechanical Engineering Department, School of Engineering, São Paulo State University (UNESP), Bauru, SP, Brazil
2. Federal Technological University of Paraná, Ponta
Interests: nonlinear dynamics; control; chaos and dynamics
Special Issues, Collections and Topics in MDPI journals
Dr. Átila Madureira Bueno

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Guest Editor
Control and Automation Engineering Department, Institute of Science and Engineering, São Paulo State University (UNESP), Sorocaba, SP, Brazil
Interests: control system; nonlinear dynamical systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Angelo Marcelo Tusset

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Guest Editor
Department of Mathematics, Federal University of Technology–Parana (UTFPR), Ponta Grossa 84016-210, Brazil
Interests: control system; nonlinear dynamical systems; robotics
Special Issues, Collections and Topics in MDPI journals
Dr. Diego Colón

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Guest Editor
Automation and Control Laboratory (LAC), Telecom and Control Department, Polytechnique School, University of São Paulo, São Paulo 05508-010, SP, Brazil
Interests: control systems; complex systems; time-delay systems; cybernetics; nonlinear dynamics; differential geometry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The SI will also be a great opportunity for disseminating recent developments of analytical and numerical techniques and for discussing novel phenomena and behaviors on 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. 

Researchers and practitioners are invited to submit their original research work on 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 practitioners’ latest unpublished work.

Prof. Dr. José Manoel Balthazar
Prof. Dr. Átila Madureira Bueno
Prof. Dr. Angelo Marcelo Tusset
Prof. Dr. Diego Colón
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. Axioms 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 and control
  • MEMs systems
  • mathematical modeling on nonlinear systems
  • numerical simulation of nonlinear systems
  • complex systems

Published Papers (3 papers)

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Research

13 pages, 4887 KiB  
Article
Fractional Dynamical Behavior of an Elastic Magneto Piezo Oscillator Including Non-Ideal Motor Excitation
by Mauricio A. Ribeiro, Jose M. Balthazar, Wagner B. Lenz, Jorge L. P. Felix, Grzegorz Litak and Angelo M. Tusset
Axioms 2022, 11(12), 667; https://doi.org/10.3390/axioms11120667 - 24 Nov 2022
Cited by 1 | Viewed by 1347
Abstract
In this work, we analyzed the nonlinear fractional dynamics in the equations of motion of a bar coupled to support under the effect of a potential described by two equally spaced magnetic poles. We also considered Bouc–Wen damping in the equations of motion. [...] Read more.
In this work, we analyzed the nonlinear fractional dynamics in the equations of motion of a bar coupled to support under the effect of a potential described by two equally spaced magnetic poles. We also considered Bouc–Wen damping in the equations of motion. For external force vibrations, we considered an equation of a non-ideal motor based on the parameters that related the interaction between the oscillation and the excitation source. With such considerations, we explored the influence of the fractional derivative operator parameter on the average power generated by the device and the dynamic behavior to determine the chaotic and periodic regions. We use Bifurcation Diagrams, Test 0–1, Phase Portrait, and Poincaré Maps. As a conclusion, we established a set of parameters for the fractional differential equations to obtain higher average powers and the periodicity windows that corroborate the establishment of energetic orbits for energy harvesting. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Chaos and Their Applications to Engineering and Science)
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21 pages, 4660 KiB  
Article
A Unified Asymptotic Theory of Supersonic, Transonic, and Hypersonic Far Fields
by Lung-Jieh Yang and Chao-Kang Feng
Axioms 2022, 11(11), 656; https://doi.org/10.3390/axioms11110656 - 19 Nov 2022
Viewed by 1040
Abstract
The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with a small thickness ratio was solved by the linearized theory, which is a first approximation at and near the surface but fails at far fields from the body. Such [...] Read more.
The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with a small thickness ratio was solved by the linearized theory, which is a first approximation at and near the surface but fails at far fields from the body. Such a problem with far fields was solved by W.D. Hayes’ “pseudo-transonic” nonlinear theory in 1954. This far field small disturbance theory is reexamined in this study first by using asymptotic expansion theory. A systematic approach is adopted to obtain the nonlinear Burgers’ equation for supersonic far fields. We also use the similarity method to solve this boundary value problem (BVP) of the inviscid Burgers’ equation and obtain the nonlinear flow patterns, including the jump condition for the shock wave. Secondly, the transonic and hypersonic far field equations were obtained from the supersonic Burgers’ equation by stretching the coordinate in the y direction and considering an expansion of the freestream Mach number in terms of the transonic and hypersonic similarity parameters. The mathematical structures of the far fields of the supersonic, transonic, and hypersonic flows are unified to be the same. The similar far field flow patterns including the shock positions of a parabolic airfoil for the supersonic, transonic, and hypersonic flow regimes are exemplified and discussed. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Chaos and Their Applications to Engineering and Science)
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38 pages, 497 KiB  
Article
A Novel Investigation of Non-Periodic Snap BVP in the G-Caputo Sense
by Xiaofeng Wang, Amel Berhail, Nora Tabouche, Mohammed M. Matar, Mohammad Esmael Samei, Mohammed K. A. Kaabar and Xiao-Guang Yue
Axioms 2022, 11(8), 390; https://doi.org/10.3390/axioms11080390 - 08 Aug 2022
Cited by 6 | Viewed by 1293
Abstract
In the present paper, we consider a nonlinear fractional snap model with respect to a G-Caputo derivative and subject to non-periodic boundary conditions. Some qualitative analysis of the solution, such as existence and uniqueness, are investigated in view of fixed-point theorems. Moreover, [...] Read more.
In the present paper, we consider a nonlinear fractional snap model with respect to a G-Caputo derivative and subject to non-periodic boundary conditions. Some qualitative analysis of the solution, such as existence and uniqueness, are investigated in view of fixed-point theorems. Moreover, the stabilities of Ulam–Hyers and Ulam–Hyers–Rassias criterions are considered and investigated. Some numerical simulations were performed using MATLAB for understanding the theoretical results. All results in this work play an important role in understanding ocean engineering phenomena due to the huge applicability of jerk and snap in seakeeping, ride comfort, and shock response spectrum. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Chaos and Their Applications to Engineering and Science)
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