Fractal Patterns In Nonlinear Dynamics And Applications

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Fractal Patterns in Nonlinear Dynamics and Applications

Santo Banerjee,M K Hassan,Sayan Mukherjee,A Gowrisankar
Fractal Patterns in Nonlinear Dynamics and Applications Book PDF

Author : Santo Banerjee,M K Hassan,Sayan Mukherjee,A Gowrisankar
Publisher : CRC Press
Page : 142 pages
File Size : 41,8 Mb
Release : 2020-03-27
Category : Mathematics
ISBN : 9781351647625

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Fractal Patterns in Nonlinear Dynamics and Applications by Santo Banerjee,M K Hassan,Sayan Mukherjee,A Gowrisankar Pdf

Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.

Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns

Santo Banerjee,A. Gowrisankar,D. Easwaramoorthy,S. Nandhini,A. Manimaran
Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns Book PDF

Author : Santo Banerjee,A. Gowrisankar,D. Easwaramoorthy,S. Nandhini,A. Manimaran
Publisher : Springer
Page : 0 pages
File Size : 41,6 Mb
Release : 2024-07-01
Category : Science
ISBN : 3031586409

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Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns by Santo Banerjee,A. Gowrisankar,D. Easwaramoorthy,S. Nandhini,A. Manimaran Pdf

This book presents selected, peer-reviewed contributions from the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems - 2023 (ISMAFDS - 2023), held at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu in India during August 24-25, 2023. It offers readers an array of captivating connections between fractal theory and nonlinear dynamics across various physics sub-domains and mathematical modeling. Fractal geometry has been developed to describe irregular natural objects that defy characterization using Euclidean geometry. Fractal techniques, such as fractal dimension and fractal functions, prove effective in mathematically modeling real-world phenomena and forecasting future consequences. The impact of fractal theory on physical sciences is widely recognized, as natural phenomena frequently exhibit fractal structures. These new concepts revolutionize our understanding of the large-scale properties of matter distribution in the universe. The book aims to familiarize readers with recent developments in common fractal patterns found in statistical physics, quantum physics, and plasma physics. Furthermore, it highlights the relationship between fractals and nonlinear dynamics through innovative approaches in mathematical modeling. This publication caters to professionals in mathematics, physics, and computer science, and also serves as a helpful resource for non-specialists seeking to comprehend fractal and nonlinear dynamics concepts. It offers valuable applications for researchers in both pure and applied backgrounds of physics and engineering.

Fractal Control and Its Applications

Shu Tang Liu,Yong Ping Zhang,Chang An Liu
Fractal Control and Its Applications Book PDF

Author : Shu Tang Liu,Yong Ping Zhang,Chang An Liu
Publisher : Springer Nature
Page : 364 pages
File Size : 51,8 Mb
Release : 2020-07-11
Category : Technology & Engineering
ISBN : 9789811554599

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Fractal Control and Its Applications by Shu Tang Liu,Yong Ping Zhang,Chang An Liu Pdf

The book focuses on fractal control and applications in various fields. Fractal phenomena occur in nonlinear models, and since the behaviors depicted by fractals need to be controlled in practical applications, an understanding of fractal control is necessary. This book introduces readers to Julia set fractals and Mandelbrot set fractals in a range of models, such as physical systems, biological systems and SIRS models, and discusses controllers designed to control these fractals. Further, it demonstrates how the fractal dimension can be calculated in order to describe the complexity of various systems.Offering a comprehensive and systematic overview of the practical issues in fractal control, this book is a valuable resource for readers interested in practical solutions in fractal control. It will also appeal to researchers, engineers, and graduate students in fields of fractal control and applications, as well as chaos control and applications.

Fractal Dimensions for Poincare Recurrences

Valentin Afraimovich,Edgardo Ugalde,Jesus Urias
Fractal Dimensions for Poincare Recurrences Book PDF

Author : Valentin Afraimovich,Edgardo Ugalde,Jesus Urias
Publisher : Elsevier
Page : 258 pages
File Size : 51,7 Mb
Release : 2006-06-21
Category : Science
ISBN : 0080462391

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Fractal Dimensions for Poincare Recurrences by Valentin Afraimovich,Edgardo Ugalde,Jesus Urias Pdf

This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the book can be used by specialists in applied nonlinear dynamics following the way in the book. The authors applied the mathematical theory developed in the book to two important problems: distribution of Poincare recurrences for nonpurely chaotic Hamiltonian systems and indication of synchronization regimes in coupled chaotic individual systems. * Portions of the book were published in an article that won the title "month's new hot paper in the field of Mathematics" in May 2004 * Rigorous mathematical theory is combined with important physical applications * Presents rules for immediate action to study mathematical models of real systems * Contains standard theorems of dynamical systems theory

Nonlinear Dynamics and Chaotic Phenomena

B.K Shivamoggi
Nonlinear Dynamics and Chaotic Phenomena Book PDF

Author : B.K Shivamoggi
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 40,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401724425

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Nonlinear Dynamics and Chaotic Phenomena by B.K Shivamoggi Pdf

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

Nonlinear Dynamics New Directions

Hernán González-Aguilar,Edgardo Ugalde
Nonlinear Dynamics New Directions Book PDF

Author : Hernán González-Aguilar,Edgardo Ugalde
Publisher : Springer
Page : 243 pages
File Size : 40,5 Mb
Release : 2015-02-10
Category : Technology & Engineering
ISBN : 9783319098647

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Nonlinear Dynamics New Directions by Hernán González-Aguilar,Edgardo Ugalde Pdf

This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynamics in biological · Includes a study of self-organized regularity in long-range systems · Explains use of Levenstein's distance for measuring lexical evolution rates

Fractal Signatures in the Dynamics of an Epidemiology

Santo Banerjee,A. Gowrisankar
Fractal Signatures in the Dynamics of an Epidemiology Book PDF

Author : Santo Banerjee,A. Gowrisankar
Publisher : CRC Press
Page : 268 pages
File Size : 45,8 Mb
Release : 2023-12-01
Category : Science
ISBN : 9781003822639

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Fractal Signatures in the Dynamics of an Epidemiology by Santo Banerjee,A. Gowrisankar Pdf

The recent Covid-19 pandemic threw the world into complete chaos with its rapid and devastating spread. Scientists are still trying to obtain a better understanding of the patterns of COVID-19 and trying to get a deeper understanding of mutant strains and their pathogenicity by performing genomic sequences of more samples. Fractal-based analysis provides its unique forecasting policy to reduce the spread of COVID-19, and in general, of any outbreaks. The book presents fractal and multifractal models of COVID-19 and reviews the impact of the pandemic including epidemiology, genome organization, transmission cycle, and control strategies based on mathematical models towards developing an immune intervention. Also, it covers non-clinical aspects such as economic development with graphical illustrations, meeting the needs of onlookers outside the sector who desire additional information on the epidemic. The fractal signatures describe the fractal textures in the patterns of Corona virus. Studies on the epidemiology of Covid-19 in relation with the fractals and fractal functions serve to exhibit its irregular chaotic nature. Moreover, the book with its wide coverage on the Hurst exponent analysis and the fractal dimension estimation, greatly aids in measuring the epidemiology.

Mathematical Modelling of Complex Patterns through Fractals and Dynamical Systems

Gowrisankar Arulprakash,Kishore Bingi,Cristina Serpa
Mathematical Modelling of Complex Patterns through Fractals and Dynamical Systems Book PDF

Author : Gowrisankar Arulprakash,Kishore Bingi,Cristina Serpa
Publisher : Springer
Page : 0 pages
File Size : 40,8 Mb
Release : 2024-09-23
Category : Computers
ISBN : 9819723426

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Mathematical Modelling of Complex Patterns through Fractals and Dynamical Systems by Gowrisankar Arulprakash,Kishore Bingi,Cristina Serpa Pdf

This book offers a wide range of interesting correlations beyond the domains of dynamical systems, complex systems, and fractal geometry. Exploring complex systems and their properties using the fractal approaches, this book provides initial solutions for new areas where fractal theory has yet to verify its expertise. Further, the book focusses on the latest scientific interest and illustrates general fractal theory in multidisciplinary areas such as computer science, electronics engineering, electrical engineering, bioengineering, biomedical, quantum physics and fluid dynamics research. This edited book is designed for professionals in the field of mathematics, computer science and physics, and even for non-specialists to help understand the concepts of fractals in nonlinear dynamical systems and complex systems while offering applications for researchers in the pure as well as in the applied background of science and engineering.

Dynamics of Fractal Surfaces

Fereydoon Family,Tam s Vicsek
Dynamics of Fractal Surfaces Book PDF

Author : Fereydoon Family,Tam s Vicsek
Publisher : World Scientific
Page : 500 pages
File Size : 49,9 Mb
Release : 1991
Category : Science
ISBN : 9810207204

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Dynamics of Fractal Surfaces by Fereydoon Family,Tam s Vicsek Pdf

In the last few years there has been an explosion of activity in the field of the dynamics of fractal surfaces, which, through the convergence of important new results from computer simulations, analytical theories and experiments, has led to significant advances in our understanding of nonequilibrium surface growth phenomena. This interest in surface growth phenomena has been motivated largely by the fact that a wide variety of natural and industrial processes lead to the formation of rough surfaces and interfaces. This book presents these developments in a single volume by bringing together the works containing the most important results in the field.The material is divided into chapters consisting of reprints related to a single major topic. Each chapter has a general introduction to a particular aspect of growing fractal surfaces. These introductory parts are included in order to provide a scientific background to the papers reproduced in the main part of the chapters. They are written in a pedagogical style and contain only the most essential information. The contents of the reprints are made more accessible to the reader as they are preceded by a short description of what the editors find to be the most significant results in the paper.

Nonlinear Dynamics and Applications

Santo Banerjee,Asit Saha
Nonlinear Dynamics and Applications Book PDF

Author : Santo Banerjee,Asit Saha
Publisher : Springer Nature
Page : 1433 pages
File Size : 52,6 Mb
Release : 2022-10-06
Category : Science
ISBN : 9783030997922

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Nonlinear Dynamics and Applications by Santo Banerjee,Asit Saha Pdf

This book covers recent trends and applications of nonlinear dynamics in various branches of society, science, and engineering. The selected peer-reviewed contributions were presented at the International Conference on Nonlinear Dynamics and Applications (ICNDA 2022) at Sikkim Manipal Institute of Technology (SMIT) and cover a broad swath of topics ranging from chaos theory and fractals to quantum systems and the dynamics of the COVID-19 pandemic. Organized by the SMIT Department of Mathematics, this international conference offers an interdisciplinary stage for scientists, researchers, and inventors to present and discuss the latest innovations and trends in all possible areas of nonlinear dynamics.

Chaotic and Fractal Dynamics

Francis C. Moon
Chaotic and Fractal Dynamics Book PDF

Author : Francis C. Moon
Publisher : John Wiley & Sons
Page : 528 pages
File Size : 43,7 Mb
Release : 2008-11-20
Category : Science
ISBN : 9783527617517

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Chaotic and Fractal Dynamics by Francis C. Moon Pdf

A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.

Dynamics with Chaos and Fractals

Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Dynamics with Chaos and Fractals Book PDF

Author : Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily
Publisher : Springer Nature
Page : 226 pages
File Size : 41,6 Mb
Release : 2020-01-01
Category : Mathematics
ISBN : 9783030358549

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Dynamics with Chaos and Fractals by Marat Akhmet,Mehmet Onur Fen,Ejaily Milad Alejaily Pdf

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.

Frontiers of Fractal Analysis

Santo Banerjee,A. Gowrisankar
Frontiers of Fractal Analysis Book PDF

Author : Santo Banerjee,A. Gowrisankar
Publisher : CRC Press
Page : 182 pages
File Size : 40,5 Mb
Release : 2022-07-07
Category : Mathematics
ISBN : 9781000625875

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Frontiers of Fractal Analysis by Santo Banerjee,A. Gowrisankar Pdf

The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

Using Time Series to Analyze Long-Range Fractal Patterns

Matthijs Koopmans
Using Time Series to Analyze Long Range Fractal Patterns Book PDF

Author : Matthijs Koopmans
Publisher : SAGE Publications
Page : 93 pages
File Size : 54,7 Mb
Release : 2020-09-23
Category : Social Science
ISBN : 9781544361437

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Using Time Series to Analyze Long-Range Fractal Patterns by Matthijs Koopmans Pdf

Using Time Series to Analyze Long Range Fractal Patterns presents methods for describing and analyzing dependency and irregularity in long time series. Irregularity refers to cycles that are similar in appearance, but unlike seasonal patterns more familiar to social scientists, repeated over a time scale that is not fixed. Until now, the application of these methods has mainly involved analysis of dynamical systems outside of the social sciences, but this volume makes it possible for social scientists to explore and document fractal patterns in dynamical social systems. Author Matthijs Koopmans concentrates on two general approaches to irregularity in long time series: autoregressive fractionally integrated moving average models, and power spectral density analysis. He demonstrates the methods through two kinds of examples: simulations that illustrate the patterns that might be encountered and serve as a benchmark for interpreting patterns in real data; and secondly social science examples such a long range data on monthly unemployment figures, daily school attendance rates; daily numbers of births to teens, and weekly survey data on political orientation. Data and R-scripts to replicate the analyses are available on an accompanying website.

Nonlinear Dynamics

Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Nonlinear Dynamics Book PDF

Author : Muthusamy Lakshmanan,Shanmuganathan Rajaseekar
Publisher : Springer Science & Business Media
Page : 644 pages
File Size : 52,9 Mb
Release : 2002-11-12
Category : Mathematics
ISBN : 3540439080

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Nonlinear Dynamics by Muthusamy Lakshmanan,Shanmuganathan Rajaseekar Pdf

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.