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Dynamics
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Theory and Applications in Nonlinear Oscillators: 2nd Edition
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Theory and Applications in Nonlinear Oscillators: 2nd Edition

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

Deadline for manuscript submissions: 30 June 2026 | Viewed by 7987

Special Issue Editor

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 are fundamental to numerous physical, chemical, biological, and mechanical systems and play a vital role in many applications. Recent research has extensively explored oscillations and vibrations, with a particular focus on the intriguing characteristics of nonlinear oscillations. These oscillations can elucidate complex phenomena and offer solutions to mechanical, electrical, and other challenges. Emerging scientific fields, such as nonlinear targeted energy transfer and hidden oscillations, highlight the dynamic nature of this research area.

This Special Issue aims to create a platform for scientists to share their latest developments, discoveries, and advancements in both the theoretical and practical aspects of nonlinear oscillators. Topics that will be covered include nonlinear oscillations, hidden attractors, energy transfer, bifurcation theory, mathematical modeling of nonlinear oscillators, synchronization and chaos control, nonlinear circuits, mechanical applications in oscillations, and more.

Dr. Christos Volos
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-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 1200 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

  • bifurcation theory
  • chaos
  • control
  • dynamical systems
  • energy transfer
  • hidden attractors
  • mathematical modeling
  • mechanical applications
  • nonlinear circuits
  • nonlinear oscillations
  • synchronization

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Published Papers (5 papers)

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31 pages, 20829 KB  
Article
FPGA Implementation of a Secure Audio Encryption System Based on Chameleon Chaotic Algorithm
by Alaa Shumran, Abdul-Basset A. Al-Hussein and Viet-Thanh Pham
Dynamics 2026, 6(1), 9; https://doi.org/10.3390/dynamics6010009 - 7 Mar 2026
Viewed by 1310
Abstract
The growing need to safeguard sensitive data in various fields, including in relation to education, banking over the phone, private voice conferences, and the military, has grown as dependence on technology in daily life has increased. Encryption schemes based on chaotic systems are [...] Read more.
The growing need to safeguard sensitive data in various fields, including in relation to education, banking over the phone, private voice conferences, and the military, has grown as dependence on technology in daily life has increased. Encryption schemes based on chaotic systems are among the most commonly utilized approaches in the security field due to their high levels of safety and reliability. This study proposes a secure audio encryption framework based on the Chameleon chaotic algorithm implemented on a Xilinx ZedBoard Zynq-7000 FPGA. The system was designed using a fixed-point arithmetic format with 32-bit precision (eight integers; 24 fractional bits) with the Xilinx System Generator in MATLAB Simulink R2021b and verified using Vivado. The Chameleon Chaotic System, characterized by its transition from self-excited to hidden attractors through parameter variation, adds complexity to the system dynamics and strengthens the encryption algorithm. The Adaptive Feedback Control technique was applied to synchronize the signals. These methods enhance the security of audio data by ensuring robust and fast synchronization during transmission. The performance of the proposed system was assessed using correlation analysis, the mean squared error, histogram analysis, and audio spectrogram analysis. The system demonstrated strong encryption capabilities with low correlation values (−0.0033). In decryption, they achieved high fidelity with a correlation exceeding 0.999 in noise-free conditions and above 0.9933 under 20 dB AWGN. Adaptive Feedback Control showed superior decryption precision with lower MSEU and higher PSNR, confirming its effectiveness under noisy environments. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)
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20 pages, 2200 KB  
Article
CMOS LIF Spiking Neuron Designed with a Memristor Emulator Based on Optimized Operational Transconductance Amplifiers
by Carlos Alejandro Velázquez-Morales, Luis Hernández-Martínez, Esteban Tlelo-Cuautle and Luis Gerardo de la Fraga
Dynamics 2025, 5(4), 54; https://doi.org/10.3390/dynamics5040054 - 18 Dec 2025
Cited by 2 | Viewed by 991
Abstract
The proposed work introduces a sizing algorithm to achieve a desired linear transconductance in the optimization of operational transconductance amplifiers (OTAs) by applying the gm/ID method to find the initial width (W) and length (L) sizes of the transistors. [...] Read more.
The proposed work introduces a sizing algorithm to achieve a desired linear transconductance in the optimization of operational transconductance amplifiers (OTAs) by applying the gm/ID method to find the initial width (W) and length (L) sizes of the transistors. These size values are used to run the non-dominated sorting genetic algorithm (NSGA-II) to perform a multi-objective optimization of three OTA topologies. The gm/ID method begins with transistor characterization using MATLAB R2024a generated look-up tables (LUTs), which map normalized transconductance of the transistor channel dimensions, and key performance metrics of a complementary metal–oxide–semiconductor (CMOS) technology. The LUTs guide the initial population generation within NSGA-II during the optimization of OTAs to achieve not only a desired transconductance but also accuracy alongside linearity, high DC gain, low power consumption, and stability. The feasible W/L size solutions provided by NSGA-II are used to enhance the CMOS design of a memristor emulator, where the OTA with the desired transconductance is adapted to tune the behavior of the memristor, demonstrating improved pinched hysteresis loop characteristics. In addition, process, voltage and temperature (PVT) variations are performed by using TSMC 180 nm CMOS technology. The memristor-based on optimized OTAs is used to design a Leaky Integrate-and-Fire (LIF) neuron, which produces identical spike counts (seven spikes) under the same input conditions, though the time period varied with a CMOS inverter scaling. It is shown that increasing transistor widths by 100 in the inverter stage, the spike quantity is altered while changing the spiking period. This highlights the role of device sizing in modulating LIF neuron dynamics, and in addition, these findings provide valuable insights for energy-efficient neuromorphic hardware design. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)
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13 pages, 1327 KB  
Article
Application of the Krylov–Bogolyubov–Mitropolsky Method to Study the Effect of Compressive (Tensile) Force on Transverse Oscillations of a Moving Nonlinear Elastic Beam
by Andrii Slipchuk, Petro Pukach and Myroslava Vovk
Dynamics 2025, 5(4), 45; https://doi.org/10.3390/dynamics5040045 - 1 Nov 2025
Cited by 1 | Viewed by 700
Abstract
The problem of nonlinear elastic transverse oscillations of a beam moving along its axis and subjected to an axial compressive or tensile force is considered. A theoretical study is carried out using the asymptotic method of nonlinear mechanics KBM (Krylov–Bogolyubov–Mitropolsky). Using this methods, [...] Read more.
The problem of nonlinear elastic transverse oscillations of a beam moving along its axis and subjected to an axial compressive or tensile force is considered. A theoretical study is carried out using the asymptotic method of nonlinear mechanics KBM (Krylov–Bogolyubov–Mitropolsky). Using this methods, differential equations were obtained in a standard form, determining the law of variation in amplitude and frequency as functions of kinematic, force, and physico-mechanical parameters in both resonant and non-resonant regimes. The fourth-order Runge–Kutta method was applied for the oscillatory system numerical analysis. The computation of complex mathematical expressions and graphical representation of the results were implemented in the mathematical software Maple 15. The results obtained can be applied for engineering calculations of structures containing moving beams subjected to compressive or tensile forces. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)
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20 pages, 4362 KB  
Article
PLC Implementation and Dynamics of a V/Heart-Shape Chaotic System
by Abdul-Basset A. Al-Hussein, Fadhil Rahma Tahir, Hamzah Abdulkareem Abbood, Mazin Majid Abdulnabi and Viet-Thanh Pham
Dynamics 2025, 5(4), 40; https://doi.org/10.3390/dynamics5040040 - 1 Oct 2025
Viewed by 2176
Abstract
This paper investigates the nonlinear dynamics behavior and practical realization of a V/Heart-shape chaotic system. Nonlinear analysis contemporary tools, including bifurcation diagram, Lyapunov exponents, phase portraits, power spectral density (PSD) bicoherence, and spectral entropy (SE), are employed to investigate the system’s complex dynamical [...] Read more.
This paper investigates the nonlinear dynamics behavior and practical realization of a V/Heart-shape chaotic system. Nonlinear analysis contemporary tools, including bifurcation diagram, Lyapunov exponents, phase portraits, power spectral density (PSD) bicoherence, and spectral entropy (SE), are employed to investigate the system’s complex dynamical behaviors. To discover the system’s versatility, two case studies are presented by varying key system parameters, revealing various strange attractors. The system is modeled and implemented using an industrial-grade programmable logic controller (PLC) with structured text (ST) language, enabling robust hardware execution. The dynamics of the chaotic system are simulated, and the results are rigorously compared with experimental data from laboratory hardware implementations, demonstrating excellent agreement. The results indicate the potential usage of the proposed chaotic system for advanced industrial applications, secure communication, and dynamic system analysis. The findings confirm the successful realization of the V-shape and Heart-shape Chaotic Systems on PLC hardware, demonstrating consistent chaotic behavior across varying parameters. This practical implementation bridges the gap between theoretical chaos research and real-world industrial applications. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)
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16 pages, 367 KB  
Article
Generalized Miller Formulae for Quantum Anharmonic Oscillators
by Maximilian T. Meyer and Arno Schindlmayr
Dynamics 2025, 5(3), 34; https://doi.org/10.3390/dynamics5030034 - 28 Aug 2025
Viewed by 1669
Abstract
Miller’s rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for [...] Read more.
Miller’s rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for the classical Lorentz model with a weak anharmonic perturbation. Recently, we developed a mathematical framework which enabled us to prove that Miller’s rule is equally valid for quantum anharmonic oscillators, despite different dynamics due to zero-point fluctuations and further quantum-mechanical effects. However, our previous derivation applied only to one-dimensional oscillators and to the special case of second- and third-harmonic generation in a monochromatic electric field. Here we extend the proof to three-dimensional quantum anharmonic oscillators and also treat all orders of the nonlinear response to an arbitrary multi-frequency field. This makes the results applicable to a much larger range of physical systems and nonlinear optical processes. The obtained generalized Miller formulae rigorously express all tensor elements of the frequency-dependent nonlinear susceptibilities in terms of the linear susceptibility and thus allow a computationally inexpensive quantitative prediction of arbitrary parametric frequency-mixing processes from a small initial dataset. Full article
(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)
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