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Special Issue "Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors II"

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

Deadline for manuscript submissions: 31 December 2019.

Special Issue Editors

Guest Editor
Ass. Prof. Christos Volos

Physics Department, Aristotle University of Thessaloniki, Greece
Website | E-Mail
Interests: physics; nonlinear circuits; chaotic cryptography; robotics
Guest Editor
Dr. Sajad Jafari

Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
E-Mail
Interests: chaos; nonlinear dynamics; optimization
Guest Editor
Dr. Jesus M. Munoz-Pacheco

Faculty of Electronics Sciences, Autonomous University of Puebla, Mexico
E-Mail
Interests: chaos theory; analog circuits; CAD; evolutionary algorithms; fractional order systems
Guest Editor
Dr. Jacques Kengne

Department of Electrical Engineering, University of Dschang, P.O. Box 134 Dschang, Cameroon
E-Mail
Interests: chaos theory; nonlinear phenomena; nonlinear circuits; hidden attractors; synchronization
Guest Editor
Dr. Karthikeyan Rajagopal

1. Center for Nonlinear dynamics, Defence University, Ethiopia
2. Institute of Energy, Mekelle University, Ethiopia
E-Mail
Interests: optimal control theory; artificial intelligence; adaptive control; neural networks

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. Sajad Jafari
Dr. Jesus M. Munoz-Pacheco
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 papers will be 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 1600 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.

Published Papers (3 papers)

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Research

Open AccessArticle
Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit
Entropy 2019, 21(7), 678; https://doi.org/10.3390/e21070678
Received: 20 May 2019 / Revised: 6 July 2019 / Accepted: 6 July 2019 / Published: 11 July 2019
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Abstract
In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC VI [...] Read more.
In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC VI (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper. Full article
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Open AccessArticle
A Class of Quadratic Polynomial Chaotic Maps and Their Fixed Points Analysis
Entropy 2019, 21(7), 658; https://doi.org/10.3390/e21070658
Received: 7 June 2019 / Revised: 28 June 2019 / Accepted: 2 July 2019 / Published: 4 July 2019
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Abstract
When chaotic systems are used in different practical applications, such as chaotic secure communication and chaotic pseudorandom sequence generators, a large number of chaotic systems are strongly required. However, for a lack of a systematic construction theory, the construction of chaotic systems mainly [...] Read more.
When chaotic systems are used in different practical applications, such as chaotic secure communication and chaotic pseudorandom sequence generators, a large number of chaotic systems are strongly required. However, for a lack of a systematic construction theory, the construction of chaotic systems mainly depends on the exhaustive search of systematic parameters or initial values, especially for a class of dynamical systems with hidden chaotic attractors. In this paper, a class of quadratic polynomial chaotic maps is studied, and a general method for constructing quadratic polynomial chaotic maps is proposed. The proposed polynomial chaotic maps satisfy the Li–Yorke definition of chaos. This method can accurately control the amplitude of chaotic time series. Through the existence and stability analysis of fixed points, we proved that such class quadratic polynomial maps cannot have hidden chaotic attractors. Full article
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Open AccessArticle
A Giga-Stable Oscillator with Hidden and Self-Excited Attractors: A Megastable Oscillator Forced by His Twin
Entropy 2019, 21(5), 535; https://doi.org/10.3390/e21050535
Received: 30 April 2019 / Revised: 20 May 2019 / Accepted: 23 May 2019 / Published: 25 May 2019
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Abstract
In this paper, inspired by a newly proposed two-dimensional nonlinear oscillator with an infinite number of coexisting attractors, a modified nonlinear oscillator is proposed. The original system has an exciting feature of having layer–layer coexisting attractors. One of these attractors is self-excited while [...] Read more.
In this paper, inspired by a newly proposed two-dimensional nonlinear oscillator with an infinite number of coexisting attractors, a modified nonlinear oscillator is proposed. The original system has an exciting feature of having layer–layer coexisting attractors. One of these attractors is self-excited while the rest are hidden. By forcing this system with its twin, a new four-dimensional nonlinear system is obtained which has an infinite number of coexisting torus attractors, strange attractors, and limit cycle attractors. The entropy, energy, and homogeneity of attractors’ images and their basin of attractions are calculated and reported, which showed an increase in the complexity of attractors when changing the bifurcation parameters. Full article
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Figure 1

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