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Fractal Patterns in Nonlinear Dynamics and Applications

Author : Santo Banerjee

Publisher : CRC Press

Page : 142 pages

File Size : 45,50 MB

Release : 2020-03-27

Category : Mathematics

ISBN : 1351647628

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Book Description

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.



Fractal Patterns in Nonlinear Dynamics and Applications

Author : Santo Banerjee

Publisher : CRC Press

Page : 207 pages

File Size : 16,15 MB

Release : 2020-03-27

Category : Mathematics

ISBN : 1498741363

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Book Description

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

Page : 0 pages

File Size : 31,47 MB

Release : 2024-07-01

Category : Science

ISBN : 9783031586408

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Book Description

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

Page : 364 pages

File Size : 37,61 MB

Release : 2020-07-11

Category : Technology & Engineering

ISBN : 9811554595

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Book Description

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.



Thinking In Patterns: Fractals And Related Phenomena In Nature

Author : Miroslav M Novak

Publisher : World Scientific

Page : 336 pages

File Size : 38,36 MB

Release : 2004-03-09

Category : Science

ISBN : 9814482846

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Book Description

Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors.This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics — from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences



Mathematical Modelling of Complex Patterns through Fractals and Dynamical Systems

Author : Gowrisankar Arulprakash

Publisher : Springer

Page : 0 pages

File Size : 36,76 MB

Release : 2024-09-23

Category : Computers

ISBN : 9789819723423

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Book Description

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.





Applications of Fractals and Chaos

Author : A.J. Crilly

Publisher : Springer Science & Business Media

Page : 312 pages

File Size : 42,78 MB

Release : 2013-11-11

Category : Computers

ISBN : 3642780970

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Book Description

Applications of Fractals and Chaos presents new developments in this rapidlydeveloping subject area. The presentation is more than merely theoretical, it specifically presents particular applications in a wide range of applications areas. Under the oceans, we consider the ways in which sponges and corals grow; we look, too, at the stability of ships on their surfaces. Land itself is modelled and applications to art, medicineand camouflage are presented. Readers should find general interest in the range of areas considered and should also be able to discover methods of value for their own specific areas of interest from studying the structure of related activities.



Nonlinear Dynamics New Directions

Author : Hernán González-Aguilar

Publisher : Springer

Page : 243 pages

File Size : 18,40 MB

Release : 2015-02-10

Category : Technology & Engineering

ISBN : 3319098640

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Book Description

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 Physiology

Author : James B. Bassingthwaighte

Publisher : Oxford University Press, USA

Page : 382 pages

File Size : 22,5 MB

Release : 1994

Category : Science

ISBN : 0195080130

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Book Description

Fractal Physiology shows how measures of the fractal properties and chaotic dynamics of cells, tissues, organs and organisms can be applied in a practical, quantitative way to studies of human physiology. The book describes in detail how to measure self-similar phenomena in order to characterize physiological phenomena such as regional blood flow variations irregularity in durations of ion channel openings and closings, and irregularities in other bioelectric signals, and how to distinguish a random signal from due to a low-order deterministic system.