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Axioms
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Advances in Theory and Applications of Chaotic and Nonlinear Dynamics
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Advances in Theory and Applications of Chaotic and Nonlinear Dynamics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 9688

Special Issue Editors

Dr. Eric Campos-Cantón

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Guest Editor
Division of Control and Dynamical Systems, Instituto Potosino Investigacion Cientifica y Tecnologica, 78216, SAN LUIS POTOSI, MEXICO
Interests: nonlinear and chaotic dynamics and their applications in science and engineering
Dr. Ernesto Zambrano-Serrano

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Guest Editor
Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, San Nicolás de los Garza 66455, Mexico
Interests: non-linear dynamics and chaos; fractional calculus; biological mathematics; engineering applications
Special Issues, Collections and Topics in MDPI journals
Dr. Guillermo Huerta Cuellar

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Guest Editor
Centro Universitario de los Lagos, Universidad de Guadalajara, Jalisco 44100, Mexico
Interests: non-linear systems; lasers dynamics; multi-stability phenomena; synchronization between a pair of chaotic oscillators
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Esteban Tlelo-Cuautle

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Guest Editor
Department of Electronics, Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Tonantinztla, Puebla 72840, Mexico
Interests: analog signal processing; integrated circuits; optimization by meta-heuristics; fractional-order chaotic systems; security in internet of things; analog/RF and mixed-signal design automation tools
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear dynamics is a useful tool in the mathematical modelling of various systems, such as electronic devices, economies, and physical processes, to mention a few. Nonlinear dynamics has had a great impact on areas of scientific research ranging from chemistry to physics and biology. Many nonlinear dynamics studies directed to the analysis of structurally stable solutions (robust stability), limit cycles, and strange attractors have been found in a wide variety of systems, including population dynamics, predator–prey models, circuit design, mechanical systems, control and automation, and neural networks. Among other dynamical behaviors, chaos has also been extensively studied in nonlinear dynamics in recent years.

Chaos refers to complex dynamic behavior modeled by nonlinear differential or difference equations. Its characteristics are very particular, such as being sensitive to initial conditions, having at least one positive Lyapunov exponent, and generating strange (self-excited or hidden) attractors. Concepts such as multistability, fractional order, variable order, and memristor-based chaos, to mention a few, have emerged in chaotic and nonlinear dynamics. Moreover, different applications have been observed as analog and digital implementations of chaotic and nonlinear systems, control, synchronization, and even complex networks with chaotic attractors in their nodes have been proposed, observing chimera states. For these reasons, we invite you to submit your research papers in the field of chaotic and nonlinear dynamics. The aim is to cover the recent advances in theoretical and numerical analysis of chaotic and nonlinear dynamics and their multidisciplinary applications.

The main topics of this Special Issue include (but are not limited to):

  • Discrete/continuous chaotic systems;
  • Hidden attractors;
  • Memristor-based chaos systems;
  • Fractional-order chaotic systems;
  • Variable-order chaotic systems;
  • Control and synchronization of chaotic systems;
  • Analog/digital circuit implementation;
  • Complex networks;
  • Chaos-based PRNG algorithms;
  • Chaos engineering applications;
  • Multistable behavior.

Dr. Eric Campos-Cantón
Dr. Ernesto Zambrano-Serrano
Dr. Guillermo Huerta Cuellar
Dr. Esteban Tlelo-Cuautle
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • hidden attractors
  • multistability
  • fractional-order systems
  • discrete/continuous chaotic systems
  • PRNG algorithms
  • synchronization

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Published Papers (5 papers)

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18 pages, 4656 KiB  
Article
Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System
by Jindong Liu, Huaigu Tian, Zhen Wang, Yan Guan and Zelin Cao
Axioms 2023, 12(12), 1125; https://doi.org/10.3390/axioms12121125 - 15 Dec 2023
Cited by 2 | Viewed by 1184
Abstract
In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional [...] Read more.
In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix. Full article
(This article belongs to the Special Issue Advances in Theory and Applications of Chaotic and Nonlinear Dynamics)
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12 pages, 2790 KiB  
Article
Solution Method for Systems of Nonlinear Fractional Differential Equations Using Third Kind Chebyshev Wavelets
by Sadiye Nergis Tural Polat and Arzu Turan Dincel
Axioms 2023, 12(6), 546; https://doi.org/10.3390/axioms12060546 - 31 May 2023
Cited by 3 | Viewed by 1232
Abstract
Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems of FDEs. The main goal of the method is to convert the nonlinear FDE into a nonlinear system of algebraic equations that can be easily solved using matrix [...] Read more.
Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems of FDEs. The main goal of the method is to convert the nonlinear FDE into a nonlinear system of algebraic equations that can be easily solved using matrix methods. In order to achieve this, we first generate the operational matrices for the fractional integration using third kind Chebyshev Wavelets and block-pulse functions (BPF) for function approximation. Since the obtained operational matrices are sparse, the obtained numerical method is fast and computationally efficient. The original nonlinear FDE is transformed into a system of algebraic equations in a vector-matrix form using the obtained operational matrices. The collocation points are then used to solve the system of algebraic equations. Numerical results for various examples and comparisons are presented. Full article
(This article belongs to the Special Issue Advances in Theory and Applications of Chaotic and Nonlinear Dynamics)
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19 pages, 1663 KiB  
Article
Bidimensional Deterministic Model for Diffusion and Settling of Particles
by Stephanie Esmeralda Velázquez Pérez, Eric Campos-Cantón, Guillermo Huerta Cuellar and Héctor Eduardo Gilardi Velázquez
Axioms 2023, 12(2), 191; https://doi.org/10.3390/axioms12020191 - 11 Feb 2023
Viewed by 1541
Abstract
In this paper, we present a study of the diffusion properties of a deterministic model for settling particles in two displacement dimensions. The particularities of the novel deterministic model include the generation of Brownian motion and a two-dimensional displacement model without stochastic processes, [...] Read more.
In this paper, we present a study of the diffusion properties of a deterministic model for settling particles in two displacement dimensions. The particularities of the novel deterministic model include the generation of Brownian motion and a two-dimensional displacement model without stochastic processes, which are governed by a set of six differential equations. This model is a piecewise system consisting of subsystems governed by jerk equations. With this model, we can consider different conditions of diffusion in both the dimensions and size of the space where the particles are dispersed. The settling time versus the dispersion medium and its size, as well as the average settling time and its probability distributions, are analyzed. Furthermore, the probability distributions for the settling location are presented for the changes in the diffusion parameters and space size. Finally, the basins of attraction for the settling positions are shown as a function of each dimensional diffusion parameter and for the medium size. Full article
(This article belongs to the Special Issue Advances in Theory and Applications of Chaotic and Nonlinear Dynamics)
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14 pages, 2387 KiB  
Article
Dynamical Analysis and Finite-Time Synchronization for a Chaotic System with Hidden Attractor and Surface Equilibrium
by Runhao Zhang, Xiaojian Xi, Huaigu Tian and Zhen Wang
Axioms 2022, 11(11), 579; https://doi.org/10.3390/axioms11110579 - 22 Oct 2022
Cited by 13 | Viewed by 1664
Abstract
In this paper, a chaotic system with surface equilibrium and a hidden attractor was studied, and the dynamical behavior, synchronization scheme and circuit application of the system were analyzed. Firstly, the stability analysis and dynamic behavior of the system were carried out (the [...] Read more.
In this paper, a chaotic system with surface equilibrium and a hidden attractor was studied, and the dynamical behavior, synchronization scheme and circuit application of the system were analyzed. Firstly, the stability analysis and dynamic behavior of the system were carried out (the type of attractor, bifurcation, Poincaré section, Lyapunov exponents spectrum and complexity). Secondly, the finite-time synchronization observer was designed according to the finite-time stability theorem to achieve the synchronization of the finite-time master–slave systems, and the error system asymptotically approached zero. Finally, the existence and practicability of the original system were proven through the implementation of the circuit system, and through using an appropriate control circuit to realize the synchronization of chaotic master–slave systems. Full article
(This article belongs to the Special Issue Advances in Theory and Applications of Chaotic and Nonlinear Dynamics)
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16 pages, 4721 KiB  
Article
Adaptive Enhancement for Coal-Rock Cutting Sound Based on Parameter Self-Tuning Bistable Stochastic Resonance Model
by Jie Xu, Jing Xu, Chaofan Ren, Yanxin Liu and Ning Sun
Axioms 2022, 11(6), 246; https://doi.org/10.3390/axioms11060246 - 25 May 2022
Viewed by 1734
Abstract
The traditional bistable stochastic resonance model has always had the drawback of being difficult when choosing accurate system parameters when a weak signal is enhanced. This paper proposes a parameter self-tuning adaptive optimization method based on the bat optimization algorithm to address this [...] Read more.
The traditional bistable stochastic resonance model has always had the drawback of being difficult when choosing accurate system parameters when a weak signal is enhanced. This paper proposes a parameter self-tuning adaptive optimization method based on the bat optimization algorithm to address this issue. The cubic mapping strategy of chaos optimization is introduced in the initial process of the individual position of the bat algorithm. Chaos is characterized by randomness, sensitivity, fractal dimension, and universality. The initial problem of the algorithm falling into local extremums is overcome. The global search capability of the basic bat optimization algorithm has been improved. The improved bat optimization algorithm’s objective function is the signal-to-noise ratio (SNR) of the target weak signal output by the bistable stochastic resonance model. An adaptive signal enhancement algorithm based on the improved bat optimization algorithm and bistable stochastic resonance (IBA-BSR) model is constructed to increase the proportion of weak signals in the mixed signal. Simulation signals are created to validate the proposed algorithm’s feasibility. The engineering application effect of this algorithm is further demonstrated by enhancing the sound signal of coal and rock cutting by a shearer in a coal face. Engineering test results demonstrate that this algorithm can significantly increase the SNR of coal and rock cutting sound signals by 42.4537 dB, and the effect is remarkable. Full article
(This article belongs to the Special Issue Advances in Theory and Applications of Chaotic and Nonlinear Dynamics)
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