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MCA
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Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics
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Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 22250

Special Issue Editor

Prof. Dr. Paweł Olejnik

E-Mail Website
Guest Editor
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski Street, 90-924 Lodz, Poland
Interests: computational techniques applied for solution of continuous and discontinuous dynamical problems and control; experimental investigations and measurements; control of linear and nonlinear dynamical systems; theory of automation and control; systems of mechatronics

Special Issue Information

Dear Colleagues,

Nonlinear dynamics takes its origins from physics and applied mathematics. In the last few decades, this interdisciplinary field of interest for many engineers, physicists, and mathematicians has spawned useful applications in almost all branches of science and technology. Looking for the closest example, well-developed asymptotic methods are among the principal methods of nonlinear analyses. Nevertheless, many theoretical and also real-world physical systems comply with interdisciplinary mathematical and numerical methods that have to be taken into account in the modeling, analysis, identification, and control of nonlinear dynamical systems, representing challenges in mathematical and computational applications.

In this Special Issue, the aim is to offer state-of-the-art current computational methods and their interdisciplinary applications oriented to solving problems in nonlinear dynamics. Potential topics include (but not limited to):

  • Mathematical modeling of physical systems,
  • Dedicated numerical methods,
  • Asymptotic methods in computations,
  • Interdisciplinary nonlinear nature of engineering problems,
  • Discontinuity driven nonlinear behavior,
  • Complex nonlinear dynamics,
  • Identification of nonlinear systems,
  • Optimization principles of nonlinear behavior,
  • Control schemes in nonlinear engineering systems,
  • Nonlinearity caused engineering problems,
  • Numerical methods in analysis of periodic and chaotic nonlinear systems.

Dr. Paweł Olejnik
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. Mathematical and Computational Applications is an international peer-reviewed open access semimonthly 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 1400 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

  • mathematical modeling
  • numerical methods
  • asymptotic methods
  • nonlinear engineering
  • discontinuous behavior
  • complex nonlinear dynamics
  • identification of parameters
  • optimization of nonlinear responses

Published Papers (6 papers)

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Editorial

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3 pages, 164 KiB  
Editorial
Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics
by Paweł Olejnik
Math. Comput. Appl. 2020, 25(4), 62; https://doi.org/10.3390/mca25040062 - 26 Sep 2020
Viewed by 1541
Abstract
Nonlinear dynamics takes its origins from physics and applied mathematics [...] Full article
(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)

Research

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15 pages, 10871 KiB  
Article
Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation
by Wojciech Śmiechowicz, Théo Loup and Paweł Olejnik
Math. Comput. Appl. 2019, 24(4), 90; https://doi.org/10.3390/mca24040090 - 16 Oct 2019
Cited by 8 | Viewed by 2621
Abstract
This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined [...] Read more.
This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions. Full article
(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)
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11 pages, 1016 KiB  
Article
On the Approximation of a Nonlinear Biological Population Model Using Localized Radial Basis Function Method
by Marjan Uddin, Hazrat Ali and Muhammad Taufiq
Math. Comput. Appl. 2019, 24(2), 54; https://doi.org/10.3390/mca24020054 - 23 May 2019
Cited by 5 | Viewed by 2386
Abstract
A localized radial basis function meshless method is applied to approximate a nonlinear biological population model with highly satisfactory results. The method approximates the derivatives at every point corresponding to their local support domain. The method is well suited for arbitrary domains. Compared [...] Read more.
A localized radial basis function meshless method is applied to approximate a nonlinear biological population model with highly satisfactory results. The method approximates the derivatives at every point corresponding to their local support domain. The method is well suited for arbitrary domains. Compared to the finite element and element free Galerkin methods, no integration tool is required. Four examples are demonstrated to check the efficiency and accuracy of the method. The results are compared with an exact solution and other methods available in literature. Full article
(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)
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21 pages, 4618 KiB  
Article
Rapid Modeling and Parameter Estimation of Partial Differential Algebraic Equations by a Functional Spreadsheet Paradigm
by Chahid Kamel Ghaddar
Math. Comput. Appl. 2018, 23(3), 39; https://doi.org/10.3390/mca23030039 - 03 Aug 2018
Cited by 2 | Viewed by 4440
Abstract
We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE). The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver. [...] Read more.
We present a systematic spreadsheet method for modeling and optimizing general partial differential algebraic equations (PDAE). The method exploits a pure spreadsheet PDAE solver function design that encapsulates the Method of Lines and permits seamless integration with an Excel spreadsheet nonlinear programming solver. Two alternative least-square dynamical minimization schemes are devised and demonstrated on a complex parameterized PDAE system with discontinues properties and coupled time derivatives. Applying the method involves no more than defining a few formulas that closely parallel the original mathematical equations, without any programming skills. It offers a simpler alternative to more complex environments which require nontrivial programming skill and effort. Full article
(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)
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21 pages, 391 KiB  
Article
Nonlinear Elimination of Drugs in One-Compartment Pharmacokinetic Models: Nonstandard Finite Difference Approach for Various Routes of Administration
by Oluwaseun Egbelowo
Math. Comput. Appl. 2018, 23(2), 27; https://doi.org/10.3390/mca23020027 - 23 May 2018
Cited by 10 | Viewed by 7780
Abstract
The motivation for this study is to introduce and motivate the use of nonstandard finite difference (NSFD) schemes, capable of solving one-compartment pharmacokinetic models. These models are modeled by both linear and nonlinear ordinary differential equations. “Exact” finite difference schemes, which are a [...] Read more.
The motivation for this study is to introduce and motivate the use of nonstandard finite difference (NSFD) schemes, capable of solving one-compartment pharmacokinetic models. These models are modeled by both linear and nonlinear ordinary differential equations. “Exact” finite difference schemes, which are a special NSFD, are provided for the linear models while we apply the NSFD rules, based on Mickens’ idea of transferring nonlinear models into discrete schemes. The method used was compared with other established methods to verify its efficiency and accuracy. One-compartment pharmacokinetic models are considered for different routes of administration: I.V. bolus injection, I.V. bolus infusion and extravascular administration. Full article
(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)
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Other

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20 pages, 2504 KiB  
Tutorial
A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping
by Roland Reginald Zana, Bálint Bodor, László Bencsik and Ambrus Zelei
Math. Comput. Appl. 2018, 23(4), 74; https://doi.org/10.3390/mca23040074 - 14 Nov 2018
Cited by 1 | Viewed by 2795
Abstract
Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low [...] Read more.
Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low DoF models of locomotion are thoroughly analyzed in the literature; however, these models do not describe the geometry accurately. We contribute by narrowing the gap between the two modeling approaches. Our goal is to develop a dynamic analysis methodology for the study of self-stable controlled multibody models of legged locomotion. An efficient way of modeling multibody systems is to use geometric constraints among the rigid bodies. It is especially effective when closed kinematic loops are present, such as in the case of walking models, when both legs are in contact with the ground. The mathematical representation of such constrained systems is the differential algebraic equation (DAE). We focus on the mathematical analysis methods of piecewise-smooth dynamic systems and we present their application for constrained multibody models of self-stable locomotion represented by DAE. Our numerical approach is demonstrated on a linear model of hopping and compared with analytically obtained reference results. Full article
(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)
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