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Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives...
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Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II

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

Deadline for manuscript submissions: closed (20 May 2022) | Viewed by 22236

Special Issue Editor

Dr. Jiri Petrzela

E-Mail Website
Guest Editor
Department of Radio Electronics, FEEC, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic
Interests: analog circuits; computer-aided analysis; chaos theory; nonlinear dynamics; numerical methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many engineering, medical, environmental, economic, social, and other observable phenomena exhibit time evolution and can be successfully modeled via suitable mathematical expression, usually in the form of a set of differential equations. Because input–output relations between system quantities are generally non-proportional, associated dynamical behavior could be very complex or, under specific conditions, chaotic. Detection, description, analysis, quantification, and control of this random-like erratic motion associated with nonlinear dynamical systems is important due to universality (through dimensionless-less mathematical modeling) and several unique properties (sensitivity to initial conditions, mixing, dense attractors, fractal dimension, long-term unpredictability, continuous frequency spectrum, etc.).

In addition to its application in information theory, entropy is a general measure, commonly used for qualitative analysis of complex systems. Similar to Lyapunov exponents or fractal dimensions, entropy describes the complexity of dynamics with respect to system parameters, external forcing, initial conditions, or time instance.

Considering the recent advances reached in the field of chaotic systems (discovery of hidden attractors, multistability, different equilibrium structures, quasi-chaotic states, etc.), this Special Issue will collect new ideas and describe promising methods arising from the field of analysis and modeling of complex nonlinear dynamical systems.

This Special Issue will accept unpublished original papers and comprehensive reviews focused on (but not restricted to) the following research areas:

  • Mathematical modeling of nature phenomena, artificial systems, and engineering problems;
  • Analysis of nonlinear dynamical systems with complex behavior;
  • New chaotic systems with special properties; both autonomous and driven;
  • Experimental investigation of nonlinear lumped networks and circuits with spread parameters;
  • Design of chaotic oscillators; described by both integer- and fractional-order;
  • Investigation of electronic systems from the viewpoint of chaos evolution;
  • Computer-aided quantification of continuous- and discrete-time dynamical flows;
  • Advanced computational algorithms applied in real problems;
  • Novel numerical methods dedicated to the qualitative analysis of dynamical flows;
  • Algorithms for analysis of time sequences and entropy calculation.

Dr. Jiri Petrzela
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 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

  • Complex systems
  • Dynamical systems
  • Entropy
  • Flow quantification
  • Chaos
  • Chaotic oscillators
  • Nonlinear circuits
  • Numerical algorithms
  • Strange attractors

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (8 papers)

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Editorial

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3 pages, 166 KiB  
Editorial
Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives
by Jiri Petrzela
Entropy 2022, 24(8), 1014; https://doi.org/10.3390/e24081014 - 22 Jul 2022
Viewed by 1335
Abstract
Biological, engineering, economic, social, medical, environmental, and other systems exhibit time evolution [...] Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)

Research

Jump to: Editorial

18 pages, 713 KiB  
Article
An Effective Synchronization Approach to Stability Analysis for Chaotic Generalized Lotka–Volterra Biological Models Using Active and Parameter Identification Methods
by Harindri Chaudhary, Ayub Khan, Uzma Nigar, Santosh Kaushik and Mohammad Sajid
Entropy 2022, 24(4), 529; https://doi.org/10.3390/e24040529 - 9 Apr 2022
Cited by 11 | Viewed by 2217
Abstract
In this manuscript, we systematically investigate projective difference synchronization between identical generalized Lotka–Volterra biological models of integer order using active control and parameter identification methods. We employ Lyapunov stability theory (LST) to construct the desired controllers, which ensures the global asymptotical convergence of [...] Read more.
In this manuscript, we systematically investigate projective difference synchronization between identical generalized Lotka–Volterra biological models of integer order using active control and parameter identification methods. We employ Lyapunov stability theory (LST) to construct the desired controllers, which ensures the global asymptotical convergence of a trajectory following synchronization errors. In addition, simulations were conducted in a MATLAB environment to illustrate the accuracy and efficiency of the proposed techniques. Exceptionally, both experimental and theoretical results are in excellent agreement. Comparative analysis between the considered strategy and previously published research findings is presented. Lastly, we describe an application of our considered combination difference synchronization in secure communication through numerical simulations. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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16 pages, 1809 KiB  
Article
Retrospective Change-Points Detection for Multidimensional Time Series of Arbitrary Nature: Model-Free Technology Based on the ϵ-Complexity Theory
by Alexandra Piryatinska and Boris Darkhovsky
Entropy 2021, 23(12), 1626; https://doi.org/10.3390/e23121626 - 2 Dec 2021
Cited by 2 | Viewed by 1554
Abstract
We consider a retrospective change-point detection problem for multidimensional time series of arbitrary nature (in particular, panel data). Change-points are the moments at which the changes in generating mechanism occur. Our method is based on the new theory of ϵ-complexity of individual [...] Read more.
We consider a retrospective change-point detection problem for multidimensional time series of arbitrary nature (in particular, panel data). Change-points are the moments at which the changes in generating mechanism occur. Our method is based on the new theory of ϵ-complexity of individual continuous vector functions and is model-free. We present simulation results confirming the effectiveness of the method. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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17 pages, 6237 KiB  
Article
Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations
by Marat Akhmet, Madina Tleubergenova and Akylbek Zhamanshin
Entropy 2021, 23(11), 1535; https://doi.org/10.3390/e23111535 - 18 Nov 2021
Cited by 16 | Viewed by 1870
Abstract
In this paper, modulo periodic Poisson stable functions have been newly introduced. Quasilinear differential equations with modulo periodic Poisson stable coefficients are under investigation. The existence and uniqueness of asymptotically stable modulo periodic Poisson stable solutions have been proved. Numerical simulations, which illustrate [...] Read more.
In this paper, modulo periodic Poisson stable functions have been newly introduced. Quasilinear differential equations with modulo periodic Poisson stable coefficients are under investigation. The existence and uniqueness of asymptotically stable modulo periodic Poisson stable solutions have been proved. Numerical simulations, which illustrate the theoretical results are provided. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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13 pages, 3249 KiB  
Article
Predictive Sequential Research Design to Study Complex Social Phenomena
by Romel Ramón González-Díaz and Gladys Inés Bustamante-Cabrera
Entropy 2021, 23(5), 627; https://doi.org/10.3390/e23050627 - 18 May 2021
Cited by 5 | Viewed by 5815
Abstract
Social phenomena in their simplest form share infinite complexities and relationships, and by interacting with other entities, their levels of complexity become exponentially inexplicable and incomprehensible. Using a single form of study in complex phenomena could be insufficient, and new forms of analysis [...] Read more.
Social phenomena in their simplest form share infinite complexities and relationships, and by interacting with other entities, their levels of complexity become exponentially inexplicable and incomprehensible. Using a single form of study in complex phenomena could be insufficient, and new forms of analysis should be opened that allow for observing the multidimensionality of study problems from integrative perspectives. The emergence of research using mixed methods attempts to reconcile these methodologies through integration, configuring a stage of interconnection between research paradigms that cause cuts and leaks that may or may not be consistent with the study’s object. At the time of integration, vices can be created by specific value and subjectivity judgments, with investigative diffraction being an alternative to extend integration through data fracture and redirecting the object of study. This work proposes a Predictive Sequential Research Design (DISPRE) for complex social phenomena, which uses fuzzy logic as a tool to solve the information biases caused by the investigative diffraction of each methodological approach as a strategy to capture, explain, understand and predict the intrinsic complexity of the social entity under study. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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15 pages, 3549 KiB  
Article
Demonstration of Three True Random Number Generator Circuits Using Memristor Created Entropy and Commercial Off-the-Shelf Components
by Scott Stoller and Kristy A. Campbell
Entropy 2021, 23(3), 371; https://doi.org/10.3390/e23030371 - 20 Mar 2021
Cited by 9 | Viewed by 3586
Abstract
In this work, we build and test three memristor-based true random number generator (TRNG) circuits: two previously presented in the literature and one which is our own design. The functionality of each circuit is assessed using the National Institute of Standards and Technology [...] Read more.
In this work, we build and test three memristor-based true random number generator (TRNG) circuits: two previously presented in the literature and one which is our own design. The functionality of each circuit is assessed using the National Institute of Standards and Technology (NIST) Statistical Test Suite (STS). The TRNG circuits were built using commercially available off-the-shelf parts, including the memristor. The results of this work confirm the usefulness of memristors for successful implementation of TRNG circuits, as well as the ease with which a TRNG can be built using simple circuit designs and off-the-shelf breadboard circuit components. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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24 pages, 35951 KiB  
Article
Evidence of Strange Attractors in Class C Amplifier with Single Bipolar Transistor: Polynomial and Piecewise-Linear Case
by Jiri Petrzela
Entropy 2021, 23(2), 175; https://doi.org/10.3390/e23020175 - 30 Jan 2021
Cited by 9 | Viewed by 2193
Abstract
This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property [...] Read more.
This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property of the analyzed structure is its bias point since the transistor is modeled via two-port admittance parameters. A necessary but not sufficient condition for the evolution of autonomous complex behavior is the nonlinear bilateral nature of the transistor with arbitrary reason that causes this effect. It is proved both by numerical analysis and experimental measurement that chaotic motion is miscellaneous, robust, and it is neither numerical artifact nor long transient motion. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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9 pages, 323 KiB  
Article
On the Possibility of Chaos in a Generalized Model of Three Interacting Sectors
by Elena V. Nikolova and Nikolay K. Vitanov
Entropy 2020, 22(12), 1388; https://doi.org/10.3390/e22121388 - 8 Dec 2020
Cited by 14 | Viewed by 2451
Abstract
In this study we extend a model, proposed by Dendrinos, which describes dynamics of change of influence in a social system containing a public sector and a private sector. The novelty is that we reconfigure the system and consider a system consisting of [...] Read more.
In this study we extend a model, proposed by Dendrinos, which describes dynamics of change of influence in a social system containing a public sector and a private sector. The novelty is that we reconfigure the system and consider a system consisting of a public sector, a private sector, and a non-governmental organizations (NGO) sector. The additional sector changes the model’s system of equations with an additional equation, and additional interactions must be taken into account. We show that for selected values of the parameters of the model’s system of equations, chaos of Shilnikov kind can exist. We illustrate the arising of the corresponding chaotic attractor and discuss the obtained results from the point of view of interaction between the three sectors. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives II)
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