Fractal Patterns In Nonlinear Dynamics And Applications

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Fractal Patterns in Nonlinear Dynamics and Applications

Author : Santo Banerjee
Publisher : CRC Press
ISBN 13 : 1351647628
Total Pages : 142 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Fractal Patterns in Nonlinear Dynamics and Applications by : Santo Banerjee

Download or read book Fractal Patterns in Nonlinear Dynamics and Applications written by Santo Banerjee and published by CRC Press. This book was released on 2020-03-27 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Santo Banerjee
Publisher : Springer
ISBN 13 : 9783031586408
Total Pages : 0 pages
Book Rating : 4.5/5 (864 download)

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Book Synopsis Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns by : Santo Banerjee

Download or read book Interplay of Fractals and Complexity in Mathematical Modelling and Physical Patterns written by Santo Banerjee and published by Springer. This book was released on 2024-07-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Shu Tang Liu
Publisher : Springer Nature
ISBN 13 : 9811554595
Total Pages : 364 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Fractal Control and Its Applications by : Shu Tang Liu

Download or read book Fractal Control and Its Applications written by Shu Tang Liu and published by Springer Nature. This book was released on 2020-07-11 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Dynamics and Applications

Author : Santo Banerjee
Publisher : Springer Nature
ISBN 13 : 3030997928
Total Pages : 1433 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Nonlinear Dynamics and Applications by : Santo Banerjee

Download or read book Nonlinear Dynamics and Applications written by Santo Banerjee and published by Springer Nature. This book was released on 2022-10-06 with total page 1433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractal Physiology and Chaos in Medicine

Author : Bruce J. West
Publisher : World Scientific
ISBN 13 : 9814417793
Total Pages : 345 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Fractal Physiology and Chaos in Medicine by : Bruce J. West

Download or read book Fractal Physiology and Chaos in Medicine written by Bruce J. West and published by World Scientific. This book was released on 2012 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exceptional book is concerned with the application of fractals and chaos, as well as other concepts from nonlinear dynamics to biomedical phenomena. Herein we seek to communicate the excitement being experienced by scientists upon making application of these concepts within the life sciences. Mathematical concepts are introduced using biomedical data sets and the phenomena being explained take precedence over the mathematics. In this new edition what has withstood the test of time has been updated and modernized; speculations that were not borne out have been expunged and the breakthroughs that have occurred in the intervening years are emphasized. The book provides a comprehensive overview of a nascent theory of medicine, including a new chapter on the theory of complex networks as they pertain to medicine.

Fractal Control Theory

Author : Shu-Tang Liu
Publisher : Springer
ISBN 13 : 9789811339097
Total Pages : 293 pages
Book Rating : 4.3/5 (39 download)

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Book Synopsis Fractal Control Theory by : Shu-Tang Liu

Download or read book Fractal Control Theory written by Shu-Tang Liu and published by Springer. This book was released on 2018-12-29 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the control of fractal behaviors in nonlinear dynamics systems, addressing both the principles and purposes of control. For fractals in different systems, it presents revealing studies on the theory and applications of control, reflecting a spectrum of different control methods used with engineering technology. As such, it will benefit researchers, engineers, and graduate students in fields of fractals, chaos, engineering, etc.

On Growth and Form

Author : Harry Eugene Stanley
Publisher : Springer Science & Business Media
ISBN 13 : 9400951655
Total Pages : 318 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis On Growth and Form by : Harry Eugene Stanley

Download or read book On Growth and Form written by Harry Eugene Stanley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have shown that simple power-law dynamics is expected for flexible fractal objects. Although the predicted behavior is well established for linear polymers, the situationm is considerably more complex for colloidal aggregates. In the latter case, the observed K-dependence of (r) can be explained either in terms of non-asymptotic hydrodynamics or in terms of weak power-law polydispersity. In the case of powders (alumina, in particular) apparent fractal behavior seen in static scattering is not found in the dynamics. ID. W. Schaefer, J. E. Martin, P. Wiitzius, and D. S. Cannell, Phys. Rev. Lett. 52,2371 (1984). 2 J. E. Martin and D. W. Schaefer, Phys. Rev. Lett. 5:1,2457 (1984). 3 D. W. Schaefer and C. C. Han in Dynamic Light Scattering, R. Pecora ed, Plenum, NY, 1985) p. 181. 4 P. Sen, this book. S J. E. Martin and B. J. Ackerson, Phys. Rev. A :11, 1180 (1985). 6 J. E. Martin, to be published. 7 D. A. Weitz, J. S. Huang, M. Y. Lin and J. Sung, Phys. Rev. Lett. 53,1657 (1984) . 8 J. E. Martin, D. W. Schaefer and A. J. Hurd, to be published; D. W. Schaefer, K. D. Keefer, J. E. Martin, and A. J. Hurd, in Physics of Finely Divided Matter, M. Daoud, Ed., Springer Verlag, NY, 1985. 9 D. W. Schaefer and A. J. Hurd, to be published. lOJ. E. Martin, J. Appl. Cryst. (to be published).

Nonlinear Dynamics

Author : Muthusamy Lakshmanan
Publisher : Springer Science & Business Media
ISBN 13 : 9783540439080
Total Pages : 644 pages
Book Rating : 4.4/5 (39 download)

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Book Synopsis Nonlinear Dynamics by : Muthusamy Lakshmanan

Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2002-11-12 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Dynamics and Chaotic Phenomena

Author : B.K Shivamoggi
Publisher : Springer Science & Business Media
ISBN 13 : 9401724423
Total Pages : 415 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Nonlinear Dynamics and Chaotic Phenomena by : B.K Shivamoggi

Download or read book Nonlinear Dynamics and Chaotic Phenomena written by B.K Shivamoggi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractal Signatures in the Dynamics of an Epidemiology

Author : Santo Banerjee
Publisher : CRC Press
ISBN 13 : 1003822630
Total Pages : 268 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Fractal Signatures in the Dynamics of an Epidemiology by : Santo Banerjee

Download or read book Fractal Signatures in the Dynamics of an Epidemiology written by Santo Banerjee and published by CRC Press. This book was released on 2023-12-01 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Dynamics and Chaos

Author : Steven H. Strogatz
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Fractal Dimensions for Poincare Recurrences

Author : Valentin Afraimovich
Publisher : Elsevier
ISBN 13 : 9780080462394
Total Pages : 258 pages
Book Rating : 4.4/5 (623 download)

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Book Synopsis Fractal Dimensions for Poincare Recurrences by : Valentin Afraimovich

Download or read book Fractal Dimensions for Poincare Recurrences written by Valentin Afraimovich and published by Elsevier. This book was released on 2006-06-21 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 New Directions

Author : Hernán González-Aguilar
Publisher : Springer
ISBN 13 : 3319098640
Total Pages : 240 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Nonlinear Dynamics New Directions by : Hernán González-Aguilar

Download or read book Nonlinear Dynamics New Directions written by Hernán González-Aguilar and published by Springer. This book was released on 2015-02-10 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Frontiers of Fractal Analysis

Author : Santo Banerjee
Publisher : CRC Press
ISBN 13 : 1000625877
Total Pages : 182 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Frontiers of Fractal Analysis by : Santo Banerjee

Download or read book Frontiers of Fractal Analysis written by Santo Banerjee and published by CRC Press. This book was released on 2022-07-07 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Matthijs Koopmans
Publisher : SAGE Publications
ISBN 13 : 1544361432
Total Pages : 93 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Using Time Series to Analyze Long-Range Fractal Patterns by : Matthijs Koopmans

Download or read book Using Time Series to Analyze Long-Range Fractal Patterns written by Matthijs Koopmans and published by SAGE Publications. This book was released on 2020-09-23 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Chaotic and Fractal Dynamics

Author : Francis C. Moon
Publisher : John Wiley & Sons
ISBN 13 : 3527617515
Total Pages : 528 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Chaotic and Fractal Dynamics by : Francis C. Moon

Download or read book Chaotic and Fractal Dynamics written by Francis C. Moon and published by John Wiley & Sons. This book was released on 2008-11-20 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data

Author : Stephen J. Guastello
Publisher : CRC Press
ISBN 13 : 1439820023
Total Pages : 631 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data by : Stephen J. Guastello

Download or read book Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data written by Stephen J. Guastello and published by CRC Press. This book was released on 2016-04-19 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflect