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Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors III

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 10075

Special Issue Editors

Dr. Christos Volos

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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
Dr. Jesus M. Munoz-Pacheco

E-Mail Website
Guest Editor
Fractional-Order Systems and Nonlinear Circuits Group, Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72570, Mexico
Interests: fractional order calculus; chaotic systems and their applications; hidden attractors; mathematical modeling; chaos theory; synchronization; random number generators
Special Issues, Collections and Topics in MDPI journals
Dr. Sajad Jafari

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Guest Editor
Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Interests: chaos; nonlinear dynamics; optimization
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Dr. Jacques Kengne

E-Mail Website
Guest Editor
Department of Electrical Engineering, University of Dschang, Dschang P.O. Box 134, Cameroon
Interests: chaos theory; nonlinear phenomena; nonlinear circuits; hidden attractors; synchronization
Special Issues, Collections and Topics in MDPI journals
Dr. Karthikeyan Rajagopal

E-Mail Website
Guest Editor
Center for Nonlinear Systems, Chennai Institute of Technology, Tamil Nadu 600069, India
Interests: optimal control theory; artificial intelligence; adaptive control; neural networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Entropy is a basic and important concept in information theory. It is also often used as a measure of the degree of chaos in dynamical systems, for example, Lyapunov exponents, fractal dimension, and entropy are usually used to describe the complexity of chaotic systems. Thus, it would be interesting to collect the latest advances in the field of studying entropy in nonlinear systems.

Additionally, in the last few years, there has been increasing interest in a new classification of nonlinear dynamical systems, including two kinds of attractors, namely: self-excited attractors and hidden attractors. Self-excited attractors can be localized straight forwardly by applying a standard computational procedure. Some interesting examples of systems with self-excited attractors are chaotic systems with different kinds of symmetry, with multi-scroll attractors, multiple attractors, and extreme multistability. On the other hand, in systems with hidden attractors, we have to develop a specific computational procedure to identify the hidden attractors because of the fact that the equilibrium points do not help in their localization. Some examples of these kinds of systems are chaotic dynamical systems with no equilibrium points, with only stable equilibria, curves of equilibria, surfaces of equilibria, and non-hyperbolic equilibria. There is evidence that hidden attractors play an important role in the various fields, ranging from phase-locked loops, oscillators describing a convective fluid motion, models of drilling systems, information theory, and cryptography to multilevel DC/DC converters. Furthermore, hidden attractors may lead to unexpected and disastrous responses. So, it is very useful to find new tools in order to study entropy for hidden attractors.

This Special Issue is dedicated to the presentation and discussion of the advanced topics of complex systems with hidden attractors and self-excited attractors. The contribution to the Special Issue should focus on the aspects of nonlinear dynamics, entropy, and applications of nonlinear systems with hidden and self-excited attractors.

Potential topics include, but are not limited to, the following:

  • Analytical–numerical methods for investing hidden oscillations
  • Bifurcation and chaos in complex systems
  • Chimera states, spiral waves, and pattern formation in networks of oscillators
  • Self-organization
  • Designing new nonlinear systems with desired features
  • Experimental study of nonlinear systems
  • Extreme multistability
  • Complex networks
  • Fractional order dynamical systems
  • Hidden attractors in complex systems
  • Entropy of hidden attractors
  • Networks of nonlinear oscillators (like neurons)
  • New methods of control and synchronization nonlinear systems
  • Information theory
  • Nonlinear dynamics and chaos in engineering applications
  • Nonlinear systems with an infinite number of equilibrium points
  • Nonlinear systems with a stable equilibrium
  • Nonlinear systems without equilibrium
  • Entropy-based cryptography
  • Novel computation algorithms for studying nonlinear systems
  • Oscillations and chaos in dynamic economic models
  • Quantum chaos
  • Related engineering applications
  • Self-excited attractors

Dr. Christos Volos
Dr. Jesus M. Munoz-Pacheco
Dr. Sajad Jafari
Dr. Jacques Kengne 
Dr. Karthikeyan Rajagopal 
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. Entropy 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 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

  • Entropy
  • Chaos
  • Complex systems
  • Nonlinear Systems
  • Hidden attractors
  • Self-excited attractors

Related Special Issues

Published Papers (4 papers)

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Research

22 pages, 950 KiB  
Article
Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique
by Jesus M. Munoz-Pacheco, Christos Volos, Fernando E. Serrano, Sajad Jafari, Jacques Kengne and Karthikeyan Rajagopal
Entropy 2021, 23(7), 921; https://doi.org/10.3390/e23070921 - 20 Jul 2021
Cited by 11 | Viewed by 2432
Abstract
In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the Cn domain. Then, [...] Read more.
In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the Cn domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors III)
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8 pages, 1573 KiB  
Article
Hidden Attractors in Discrete Dynamical Systems
by Marek Berezowski and Marcin Lawnik
Entropy 2021, 23(5), 616; https://doi.org/10.3390/e23050616 - 16 May 2021
Cited by 3 | Viewed by 2057
Abstract
Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on [...] Read more.
Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors III)
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20 pages, 4084 KiB  
Article
A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies
by Hua Wang, Hadi Jahanshahi, Miao-Kun Wang, Stelios Bekiros, Jinping Liu and Ayman A. Aly
Entropy 2021, 23(5), 610; https://doi.org/10.3390/e23050610 - 14 May 2021
Cited by 34 | Viewed by 2518
Abstract
Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the [...] Read more.
Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors III)
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26 pages, 7271 KiB  
Article
Image Encryption Scheme with Compressed Sensing Based on a New Six-Dimensional Non-Degenerate Discrete Hyperchaotic System and Plaintext-Related Scrambling
by Chunyang Sun, Erfu Wang and Bing Zhao
Entropy 2021, 23(3), 291; https://doi.org/10.3390/e23030291 - 27 Feb 2021
Cited by 22 | Viewed by 2040
Abstract
Digital images can be large in size and contain sensitive information that needs protection. Compression using compressed sensing performs well, but the measurement matrix directly affects the signal compression and reconstruction performance. The good cryptographic characteristics of chaotic systems mean that using one [...] Read more.
Digital images can be large in size and contain sensitive information that needs protection. Compression using compressed sensing performs well, but the measurement matrix directly affects the signal compression and reconstruction performance. The good cryptographic characteristics of chaotic systems mean that using one to construct the measurement matrix has obvious advantages. However, existing low-dimensional chaotic systems have low complexity and generate sequences with poor randomness. Hence, a new six-dimensional non-degenerate discrete hyperchaotic system with six positive Lyapunov exponents is proposed in this paper. Using this chaotic system to design the measurement matrix can improve the performance of image compression and reconstruction. Because image encryption using compressed sensing cannot resist known- and chosen-plaintext attacks, the chaotic system proposed in this paper is introduced into the compressed sensing encryption framework. A scrambling algorithm and two-way diffusion algorithm for the plaintext are used to encrypt the measured value matrix. The security of the encryption system is further improved by generating the SHA-256 value of the original image to calculate the initial conditions of the chaotic map. A simulation and performance analysis shows that the proposed image compression-encryption scheme has high compression and reconstruction performance and the ability to resist known- and chosen-plaintext attacks. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors III)
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