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Replication of Chaos in Neural Networks, Economics and Physics

Author: Marat Akhmet

Publisher: Springer

Published: 2015-08-13

Total Pages: 457

ISBN-13: 3662475006

This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.

Dynamics with Chaos and Fractals

Author: Marat Akhmet

Publisher: Springer Nature

Published: 2020-01-01

Total Pages: 226

ISBN-13: 3030358542

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The book is concerned with the concepts of chaos and fractals, which are within the scopes of dynamical systems, geometry, measure theory, topology, and numerical analysis during the last several decades. It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. This is the first time in the literature that the description of chaos is initiated from a single motion. Chaos is now placed on the line of oscillations, and therefore, it is a subject of study in the framework of the theories of dynamical systems and differential equations, as in this book. The techniques introduced in the book make it possible to develop continuous and discrete dynamics which admit fractals as points of trajectories as well as orbits themselves. To provide strong arguments for the genericity of chaos in the real and abstract universe, the concept of abstract similarity is suggested.

Handbook of Research on Modeling, Analysis, and Control of Complex Systems

Author: Azar, Ahmad Taher

Publisher: IGI Global

Published: 2020-12-05

Total Pages: 685

ISBN-13: 1799857905

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The current literature on dynamic systems is quite comprehensive, and system theory’s mathematical jargon can remain quite complicated. Thus, there is a need for a compendium of accessible research that involves the broad range of fields that dynamic systems can cover, including engineering, life sciences, and the environment, and which can connect researchers in these fields. The Handbook of Research on Modeling, Analysis, and Control of Complex Systems is a comprehensive reference book that describes the recent developments in a wide range of areas including the modeling, analysis, and control of dynamic systems, as well as explores related applications. The book acts as a forum for researchers seeking to understand the latest theory findings and software problem experiments. Covering topics that include chaotic maps, predictive modeling, random bit generation, and software bug prediction, this book is ideal for professionals, academicians, researchers, and students in the fields of electrical engineering, computer science, control engineering, robotics, power systems, and biomedical engineering.

Differential and Difference Equations with Applications

Author: Sandra Pinelas

Publisher: Springer Nature

Published: 2020-10-21

Total Pages: 754

ISBN-13: 3030563235

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This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

Integration of Fuzzy Logic and Chaos Theory

Author: Zhong Li

Publisher: Springer Science & Business Media

Published: 2006-01-10

Total Pages: 620

ISBN-13: 3540268995

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This book attempts to present some current research progress and results on the interplay of fuzzy logic and chaos theory. More specifically, this book includes a collection of some state-of-theart surveys, tutorials, and application examples written by some experts working in the interdisciplinary fields overlapping fuzzy logic and chaos theory. The content of the book covers fuzzy definition of chaos, fuzzy modeling and control of chaotic systems using both Mamdani and Takagi-Sugeno models, fuzzy model identification using genetic algorithms and neural network schemes, bifurcation phenomena and self-referencing in fuzzy systems, complex fuzzy systems and their collective behaviours, as well as some applications of combining fuzzy logic and chaotic dynamics, such as fuzzy-chaos hybrid controllers for nonlinear dynamic systems, and fuzzy-model-based chaotic cryptosystems. This book can serve as a handy reference for researchers working in interdisciplines related, among others, to both fuzzy logic and chaos theory.

Chaos and Complex Systems

Author: Stavros G. Stavrinides

Publisher: Springer Nature

Published: 2020-02-19

Total Pages: 169

ISBN-13: 3030354415

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This book presents the proceedings of the “5th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (CCS).” All Symposia in the series bring together scientists, engineers, economists and social scientists, creating a vivid forum for discussions on the latest insights and findings obtained in the areas of complexity, nonlinear dynamics and chaos theory, as well as their interdisciplinary applications. The scope of the latest Symposium was enriched with a variety of contemporary, interdisciplinary topics, including but not limited to: fundamental theory of nonlinear dynamics, networks, circuits, systems, biology, evolution and ecology, fractals and pattern formation, nonlinear time series analysis, neural networks, sociophysics and econophysics, complexity management and global systems.

Chaos Theory in the Social Sciences

Author: L. Douglas Kiel

Publisher: University of Michigan Press

Published: 1997-09-26

Total Pages: 364

ISBN-13: 9780472084722

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Dynamics of Markets

Author: Joseph L. McCauley

Publisher: Cambridge University Press

Published: 2004-05-06

Total Pages: 246

ISBN-13: 9780521824477

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Text introducing a new empirically-based model of financial market dynamics.

Chaos Theory in Economics

Author: W. Davis Dechert

Publisher:

Published: 1996

Total Pages: 632

ISBN-13:

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A collection of essays which bring together three basic aspects of research into nonlinear dynamics and economics. The first papers deal with the theoretical methods used in analyzing chaotic dynamics and the statistical tools to detect the presence of non-linearities in economic data. The following articles discuss the models which are currently being used to stimulate nonlinear economic phenomena. The final papers apply these methods to a number of economic time series.

Chaos and Non-linear Models in Economics

Author: John Creedy

Publisher:

Published: 1994

Total Pages: 228

ISBN-13:

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