Fractal Patterns In Nonlinear Dynamics And Applications
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Fractal Patterns In Nonlinear Dynamics And Applications
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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2020-03-27
Fractal Patterns In Nonlinear Dynamics And Applications written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-27 with Mathematics categories.
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
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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2020-03-27
Fractal Patterns In Nonlinear Dynamics And Applications written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-27 with Mathematics categories.
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.
Proceedings Of The 2nd International Conference On Nonlinear Dynamics And Applications Icnda 2024 Volume 2
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Author : Asit Saha
language : en
Publisher: Springer Nature
Release Date : 2024-10-10
Proceedings Of The 2nd International Conference On Nonlinear Dynamics And Applications Icnda 2024 Volume 2 written by Asit Saha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-10 with Science categories.
This book covers the latest advancements and applications of nonlinear dynamics in various fields of science and engineering, presenting a curated selection of peer-reviewed contributions at the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024) at Sikkim Manipal Institute of Technology (SMIT). Organized by the Department of Mathematics, SMIT, SMU, this international conference provides a platform for scientists, researchers, and inventors to share their findings and exchange ideas in the ever-evolving field of nonlinear dynamics. This book comprises three volumes. Volume 2 focuses on chaos, complexity, and fractals in dynamical systems. It covers topics such as novel methods for solving population balance models; analysis of fractal structures and nonlinear partial differential equations; dynamics of disease therapy and cytokine interactions; stability and behavior of predator-prey and ecological systems; fluid dynamics and heat transfer in nanofluids; and numerical and analytical approaches to material and structural optimization
Thinking In Patterns
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Author : Miroslav Michal Novak
language : en
Publisher: World Scientific
Release Date : 2004
Thinking In Patterns written by Miroslav Michal Novak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
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
Interplay Of Fractals And Complexity In Mathematical Modelling And Physical Patterns
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Author : Santo Banerjee
language : en
Publisher: Springer Nature
Release Date : 2025-03-07
Interplay Of Fractals And Complexity In Mathematical Modelling And Physical Patterns written by Santo Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-07 with Science categories.
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.
Frontiers Of Fractal Analysis
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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2022-07-07
Frontiers Of Fractal Analysis written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-07 with Mathematics categories.
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.
Nonlinear Dynamics And Chaos
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Chaos written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
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.
Using Time Series To Analyze Long Range Fractal Patterns
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Author : Matthijs Koopmans
language : en
Publisher: SAGE Publications
Release Date : 2020-09-23
Using Time Series To Analyze Long Range Fractal Patterns written by Matthijs Koopmans and has been published by SAGE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Social Science categories.
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.
Fractal Functions Dimensions And Signal Analysis
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Author : Santo Banerjee
language : en
Publisher: Springer Nature
Release Date : 2020-12-14
Fractal Functions Dimensions And Signal Analysis written by Santo Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Science categories.
This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.
Fractal Physiology And Chaos In Medicine
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Author : Bruce J. West
language : en
Publisher: World Scientific
Release Date : 2012
Fractal Physiology And Chaos In Medicine written by Bruce J. West and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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.