Editorial

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Open AccessEditorial

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

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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

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18 pages, 713 KiB

Open AccessArticle

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 - 09 Apr 2022

Cited by 10 | Viewed by 1768

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

Open AccessArticle

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 - 02 Dec 2021

Cited by 2 | Viewed by 1234

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

Open AccessArticle

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 1450

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

Open AccessArticle

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 4 | Viewed by 4161

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

Open AccessArticle

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 2922

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

Open AccessArticle

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 8 | Viewed by 1781

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

Open AccessArticle

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 - 08 Dec 2020

Cited by 10 | Viewed by 2142

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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