Special Issue "Numerical Computation and Nonlinear Dynamical Systems"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 August 2019).

Special Issue Editor

Prof. Simone Fiori
E-Mail Website
Guest Editor
Department of Information Engineering, Marches Polytechnic University, Via Brecce Bianche, Ancona I-60131, Italy
Interests: nonlinear statistical modeling of monotonic as well as nonmonotonic relationship between two random variables on the basis of complete or incomplete data pairs; computing statistical descriptors of random distributions on curved spaces
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Special Issue Information

Dear Colleagues,

Non-linear problems are of interest to engineers, biologists, physicists, and mathematicians. because most real-world systems are inherently non-linear. In particular, non-linear dynamical systems describe changes in variables over time governed by complicated non-linear functions, and may result in complex and chaotic trajectories over the state space. A class of non-linear dynamical systems arise when non-linear constraints exist between the variables, which may be framed in the context of dynamical systems on manifolds.

Non-linear dynamical systems are notoriously difficult to study and to solve precisely, therefore, it is customary to resort to numerical approximations for their exact solutions. A common approximated approach is based on local linearization. This approach works well up to a certain accuracy and some range for the input values, but some interesting phenomena, such as solitons, chaos, and singularities, are hidden by linearization. More sophisticated approaches have been developed over the years to study the features and to approximate the solutions of non-linear dynamical systems, under the form of non-linear numerical methods. The aim of the present Special Issue is to present the latest results in the modeling of real-world engineering or applied-science phenomena by non-linear dynamical systems, in the study of formal theories to characterize the behavior of non-linear dynamical systems (for example in chaotic systems), in the numerical simulation of the behavior of non-linear dynamical systems (for example, by geometric-integration methods), and in the control of non-linear dynamical systems (with special emphasis on non-linear feedback control).

Prof. Dr. Simone Fiori
Guest Editor

Manuscript Submission Information

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Keywords

  • non-linear dynamical system
  • numerical computational method
  • modelling of complex real-world phenomenon
  • optimization problem solving by non-linear dynamics
  • non-linear feedback control

Published Papers (2 papers)

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Research

Open AccessArticle
Global Analysis and the Periodic Character of a Class of Difference Equations
Axioms 2019, 8(4), 131; https://doi.org/10.3390/axioms8040131 - 15 Nov 2019
Abstract
In biology, difference equations is often used to understand and describe life phenomenon through mathematical models. So, in this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. [...] Read more.
In biology, difference equations is often used to understand and describe life phenomenon through mathematical models. So, in this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May’s Host Parasitoid Model, as a special case. Full article
(This article belongs to the Special Issue Numerical Computation and Nonlinear Dynamical Systems)
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Open AccessArticle
Advanced Control Strategies to Improve Nonlinear Automotive Dynamical Systems Consumption
Axioms 2019, 8(4), 123; https://doi.org/10.3390/axioms8040123 - 01 Nov 2019
Abstract
Electric motors and Internal Combustion Engine test benches allow for testing, under various conditions, the behavior of the Electric Vehicles and they are essential in the automotive field development. In this paper, we introduce the state-of-art of the control algorithms and their validation [...] Read more.
Electric motors and Internal Combustion Engine test benches allow for testing, under various conditions, the behavior of the Electric Vehicles and they are essential in the automotive field development. In this paper, we introduce the state-of-art of the control algorithms and their validation over different test runs, on the standard driving cycles. Ad-hoc simulations and test benches designed for the issue offer a significant opportunity to reduce costs. The modelling of automotive systems is a non-trivial problem due to the non-linearities. The paper presents a linearized solution and an adaptive control scheme to improve model performances starting from real data, and also discusses the behavior of the proposed system and the control law reporting emissions of the considered virtual vehicle when compared with the target emission regulations. Full article
(This article belongs to the Special Issue Numerical Computation and Nonlinear Dynamical Systems)
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