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Mathematics
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Analytical Approaches to Nonlinear Dynamical Systems and Applications, 4th Edition
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Analytical Approaches to Nonlinear Dynamical Systems and Applications, 4th Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 31 March 2027 | Viewed by 544

Editor

Prof. Dr. Nicolae Herisanu

E-Mail Website
Guest Editor
Faculty of Mechanics, University Politehnica Timisoara, 300222 Timisoara, Romania
Interests: nonlinear dynamical systems; rotating electric machines
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of Mathematics aims to explore the analytical methodologies that provide profound insights into the complexities of nonlinear dynamical systems. We invite contributions that highlight recent advancements and emerging trends in the analytical study of these systems, particularly those described by nonlinear differential equations.

We encourage submissions that present innovative analytical treatments of nonlinear dynamical systems, showcasing applications across diverse fields such as physics, applied mathematics, mechanics, engineering and life sciences. Interdisciplinary approaches that illustrate potential future research directions are also highly welcome. This Special Issue seeks to foster a deeper understanding of nonlinear phenomena and to inspire further exploration in this vital area of study.

Prof. Dr. Nicolae Herisanu
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics 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 2600 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

  • dynamical systems
  • nonlinear phenomena
  • analytical methods
  • nonlinear differential equations
  • approximate analytical solutions

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Related Special Issue

Published Papers (2 papers)

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Research

21 pages, 2095 KB  
Article
A Toolface Prediction Model Considering Nonlinear Wellbore Friction for Directional Coring Drilling Tool
by Lingda Hu, Lu Wang, Yutong Zu and Xiaochun Ma
Mathematics 2026, 14(16), 2945; https://doi.org/10.3390/math14162945 - 14 Aug 2026
Abstract
In directional coring drilling, toolface adjustment is performed during drilling interruption by rotating the drill string through the top drive. Because the bottom-hole toolface angle cannot be transmitted to the surface in real time, a dynamic prediction model is required to guide toolface [...] Read more.
In directional coring drilling, toolface adjustment is performed during drilling interruption by rotating the drill string through the top drive. Because the bottom-hole toolface angle cannot be transmitted to the surface in real time, a dynamic prediction model is required to guide toolface control. Existing flexible drill string models, however, generally neglect the nonlinear wellbore friction caused by stick–slip motion, reducing prediction accuracy. To address this issue, a distributed-parameter torsional dynamic model is established and discretized into a multi-degree-of-freedom system. A friction-state-based prediction–correction iterative algorithm is proposed to resolve the strong coupling between wellbore friction and system dynamics. At each time step, the sticking or slipping state is identified from the predicted motion, and the wellbore friction torque is iteratively updated until the friction state and dynamic equilibrium simultaneously converge, enabling accurate prediction of the drill bit toolface angle. Simulation results show that the proposed model captures the key dynamic characteristics of toolface adjustment. Under typical operating conditions, the drill bit start-up delay is 3.53 s, the peak angular velocity reaches 1.73°/s, and the peak transmitted torque is 2.28 kN·m. After the top drive stops, the drill bit continues rotating because of inertia, resulting in a 2.12° toolface overshoot and an angular lag rate of 21.2%. In addition, the effects of weight on bit, top-drive speed, and equivalent damping on toolface adjustment are quantified, providing guidance for parameter optimization. The proposed method provides a theoretical basis for toolface prediction and control in intelligent directional coring drilling. Full article
(This article belongs to the Special Issue Analytical Approaches to Nonlinear Dynamical Systems and Applications, 4th Edition)
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21 pages, 16632 KB  
Article
Variable-Order Fractional Calculus-Based Chaos Analysis of a Novel Eight-Dimensional Hyperchaotic System
by Khaled Helmi Khashan, Diaa Eldin Elgezouli and Mohamed A. Abdoon
Mathematics 2026, 14(15), 2674; https://doi.org/10.3390/math14152674 - 24 Jul 2026
Viewed by 336
Abstract
In this study, we develop a novel variable-order fractional extension of an eight-dimensional (8D) hyperchaotic differential equation system modeled via the Liouville–Caputo operator. Moving beyond constant fractional-order models, our system implements time-variable orders, which enable its historical memory structure to evolve dynamically over [...] Read more.
In this study, we develop a novel variable-order fractional extension of an eight-dimensional (8D) hyperchaotic differential equation system modeled via the Liouville–Caputo operator. Moving beyond constant fractional-order models, our system implements time-variable orders, which enable its historical memory structure to evolve dynamically over time. To numerically approximate the trajectories of this complex 8D system, a second-order Lagrange numerical integration approach is formulated. An extensive dynamic analysis explores the behavior of this variable-order framework under two distinct configurations: a slowly periodic memory function and a smooth, monotonic hyperbolic tangent function. Topological complexity and multidimensional chaos are characterized using parameter-dependent bifurcation diagrams, phase portraits, Kaplan–Yorke fractal dimensions, and Kolmogorov–Sinai metric entropy. Numerical results show that both variable-order configurations display robust hyperchaotic dynamics characterized by four positive Lyapunov exponents. Crucially, the proposed variable-order extension enhances the phase space footprint of the baseline system, achieving a maximum Kaplan–Yorke dimension of 7.100, thereby offering excellent topological density for secure cryptographic applications. Full article
(This article belongs to the Special Issue Analytical Approaches to Nonlinear Dynamical Systems and Applications, 4th Edition)
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