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Dynamics
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Theory and Applications in Nonlinear Oscillators
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Theory and Applications in Nonlinear Oscillators

A special issue of Dynamics (ISSN 2673-8716).

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 4240

Special Issue Editors

Dr. Jamal Odysseas Maaita

E-Mail Website
Guest Editor
1. School of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
2. Physics Department, International Hellenic University, Kavala 65404, Greece
Interests: oscillations; nonlinear dynamics; chaotic dynamics; mechanics; nonlinear electrical circuits
Dr. Christos Volos

E-Mail Website
Guest Editor
Laboratory of Nonlinear Systems, Circuits & Coplexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece
Interests: electrical and electronics engineering; mathematical modeling; control theory; engineering, applied and computational mathematics; numerical analysis; mathematical analysis; numerical modeling; modeling and simulation; robotics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Oscillations play an essential role in many physical systems and many applications. In recent years, many scientists have done a great deal of work studying oscillations and vibrations. In particular, non-linear oscillations present exciting characteristics that can describe complex phenomena or solve mechanical, electrical, and other problems. New scientific areas arise, such as non-linear targeted energy transfer or hidden oscillations.

This Special Issue aims to provide a space where scientists share their recent developments, discoveries, and progress, both in theory and applications, in the field of non-linear oscillators. The topics of the issue include non-linear oscillations, hidden attractors, energy transfer, bifurcation theory, mathematical modeling of non-linear oscillators, synchronization and chaos control, non-linear electronic circuits, mechanical applications in oscillations, and others.

Dr. Jamal Odysseas Maaita
Prof. Dr. Christos Volos
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. Dynamics is an international peer-reviewed open access quarterly 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 1000 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

  • non-linear oscillations
  • chaos
  • dynamical systems
  • non-linear electronic circuits
  • hidden attractors
  • energy transfer
  • mathematical modeling
  • bifurcation theory
  • control
  • synchronization

Published Papers (2 papers)

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Research

19 pages, 4013 KiB  
Article
Dynamics Differences between Minimal Models of Second and First-Order Chemical Self-Replication
by Lauren A. Moseley and Enrique Peacock-López
Dynamics 2023, 3(3), 425-443; https://doi.org/10.3390/dynamics3030023 - 03 Aug 2023
Viewed by 755
Abstract
To further explore the origins of Life, we consider three self-replicating chemical models. In general, models of the origin of Life include molecular components that can self-replicate and achieve exponential growth. Therefore, chemical self-replication is an essential chemical property of any model. The [...] Read more.
To further explore the origins of Life, we consider three self-replicating chemical models. In general, models of the origin of Life include molecular components that can self-replicate and achieve exponential growth. Therefore, chemical self-replication is an essential chemical property of any model. The simplest self-replication mechanisms use the molecular product as a template for its synthesis. This mechanism is the so-called First-Order self-replication. Its regulatory limitations make it challenging to develop chemical networks, which are essential in the models of the origins of Life. In Second-Order self-replication, the molecular product forms a catalytic dimer capable of synthesis of the principal molecular product. In contrast with a simple template, the dimers show more flexibility in forming complex chemical networks since the chemical activity of the dimers can be activated or inhibited by the molecular components of the network. Here, we consider three minimal models: the First-Order Model (FOM), the Second-Order Model (SOM), and an Extended Second-Order Model (ESOM). We construct and analyze the mechanistic dimensionless ordinary differential equations (ODEs) associated with the models. The numerical integration of the set of ODEs gives us a visualization of these systems’ oscillatory behavior and compares their capacities for sustained autocatalytic behavior. The FOM model displays more complex oscillatory behavior than the ESOM model. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators)
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12 pages, 3283 KiB  
Article
Chaotic van der Pol Oscillator Control Algorithm Comparison
by Lauren Ribordy and Timothy Sands
Dynamics 2023, 3(1), 202-213; https://doi.org/10.3390/dynamics3010012 - 19 Mar 2023
Cited by 1 | Viewed by 2158
Abstract
The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Controlling, or forcing, the behavior of a van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting [...] Read more.
The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Controlling, or forcing, the behavior of a van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the van der Pol oscillator. Deterministic artificial intelligence is a feedforward and feedback control method that leverages the known physics of the van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of deterministic artificial intelligence employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error between the target trajectory and the response oscillator trajectory over time. Two algorithms performed better than the benchmark with necessary discussion of the conditions under which they perform best. Recursive least squares with exponential forgetting had the lowest mean absolute error overall, with a 2.46% reduction in error compared to the baseline, feedforward without deterministic artificial intelligence. While least mean squares with normalized gradient adaptation had worse initial error in the first 10% of the simulation, after that point it exhibited consistently lower error. Over the last 90% of the simulation, deterministic artificial intelligence with least mean squares with normalized gradient adaptation achieved a 48.7% reduction in mean absolute error compared to baseline. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators)
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