Santo Banerjee's Books

Fractal Functions, Dimensions and Signal Analysis

By: Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar

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Fractal Functions, Dimensions and Signal Analysis

By: Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar

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.

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Page Count

132

Publisher

Springer Nature

Published Date

ISBN 10

3030626725

ISBN 13

9783030626723

Introduction to Nonlinear Circuits and Networks

By: Bharathwaj Muthuswamy,Santo Banerjee

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Introduction to Nonlinear Circuits and Networks

By: Bharathwaj Muthuswamy,Santo Banerjee

This course-based text revisits classic concepts in nonlinear circuit theory from a very much introductory point of view: the presentation is completely self-contained and does not assume any prior knowledge of circuit theory. It is simply assumed that readers have taken a first-year undergraduate course in differential and integral calculus, along with an elementary physics course in classical mechanics and electrodynamics. Further, it discusses topics not typically found in standard textbooks, such as nonlinear operational amplifier circuits, nonlinear chaotic circuits and memristor networks. Each chapter includes a set of illustrative and worked examples, along with end-of-chapter exercises and lab exercises using the QUCS open-source circuit simulator. Solutions and other material are provided on the YouTube channel created for this book by the authors.

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Page Count

373

Publisher

Springer

Published Date

ISBN 10

3319673254

ISBN 13

9783319673257

Dynamical Systems and Nonlinear Waves in Plasmas

By: Santo Banerjee,Asit Saha

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Dynamical Systems and Nonlinear Waves in Plasmas

By: Santo Banerjee,Asit Saha

Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.

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Page Count

207

Publisher

CRC Press

Published Date

ISBN 10

1000404765

ISBN 13

9781000404760

Fractal Patterns with MATLAB

By: Santo Banerjee,A. Gowrisankar,Komandla Mahipal Reddy

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Fractal Patterns with MATLAB

By: Santo Banerjee,A. Gowrisankar,Komandla Mahipal Reddy

This book presents the iterative beauty of fractals and fractal functions graphically with the aid of MATLAB programming. The fractal images generated using the MATLAB codes provide visual delight and highly encourage the fractal lovers for creative thinking. The book compiles five cutting-edge research chapters, each with state-of-the art fractal illustrations. It starts with the fundamental theory for the construction of fractal sets via the deterministic iteration algorithm. Incorporating the theoretical base, fractal illustrations of elementary fractal sets are provided with the explicit MATLAB code. The book gives examples of MATLAB codes to present the fractal surfaces. This book is contributed to all the research beginners as well as the professionals on the field of fractal analysis. As it covers basic fractals like Sierpinski triangle to advanced fractal functions with explicit MATLAB code, the presented fractal illustrations hopefully benefit even the non-field readers. The book is a useful course to all the research beginners on the fractal and fractal-related fields.

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Springer Nature

Published Date

ISBN 10

303148102X

ISBN 13

9783031481024

A Route to Chaos Using FPGAs

Volume I: Experimental Observations

By: Bharathwaj Muthuswamy,Santo Banerjee

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A Route to Chaos Using FPGAs

Volume I: Experimental Observations

By: Bharathwaj Muthuswamy,Santo Banerjee

The purpose of this introductory book is to couple the teaching of chaotic circuit and systems theory with the use of field programmable gate arrays (FPGAs). As such, it differs from other texts on chaos: first, it puts emphasis on combining theoretical methods, simulation tools and physical realization to help the reader gain an intuitive understanding of the properties of chaotic systems. Second, the "medium" used for physical realization is the FPGA. These devices are massively parallel architectures that can be configured to realize a variety of logic functions. Hence, FPGAs can be configured to emulate systems of differential equations. Nevertheless maximizing the capabilities of an FPGA requires the user to understand the underlying hardware and also FPGA design software. This is achieved by the third distinctive feature of this book: a lab component in each chapter. Here, readers are asked to experiment with computer simulations and FPGA designs, to further their understanding of concepts covered in the book. This text is intended for graduate students in science and engineering interested in exploring implementation of nonlinear dynamical (chaotic) systems on FPGAs.

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Page Count

234

Publisher

Springer

Published Date

ISBN 10

331918105X

ISBN 13

9783319181059

Fractal Patterns in Nonlinear Dynamics and Applications

By: Santo Banerjee,M K Hassan,Sayan Mukherjee,A Gowrisankar

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Fractal Patterns in Nonlinear Dynamics and Applications

By: Santo Banerjee,M K Hassan,Sayan Mukherjee,A Gowrisankar

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.

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Page Count

207

Publisher

CRC Press

Published Date

ISBN 10

1498741363

ISBN 13

9781498741361

Chaotic Dynamics of Fractional Discrete Time Systems

By: Vignesh Dhakshinamoorthy,Guo-Cheng Wu,Santo Banerjee

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Chaotic Dynamics of Fractional Discrete Time Systems

By: Vignesh Dhakshinamoorthy,Guo-Cheng Wu,Santo Banerjee

The book reviews the application of discrete fractional operators in diverse fields such as biological and chemical reactions, as well as chaotic systems, demonstrating their applications in physics. The dynamical analysis is carried out using equilibrium points of the system for studying their stability properties and the chaotic behaviors are illustrated with the help of bifurcation diagrams and Lyapunov exponents. The book is divided into three parts. Part I deals with the application of discrete fractional operators in chemical reaction-based systems with biological significance. Two different chemical reaction models are analysed- one being disproportionation of glucose, which plays an important role in human physiology and the other is the Lengyel – Epstein chemical model. Chaotic behavior of the systems is studied and the synchronization of the system is performed. Part II covers the analysis of biological systems like tumor immune system and neuronal models by introducing memristor based flux control. The memductance functions are considered as quadratic, periodic, and exponential functions. The final part of the book reviews the complex form of the Rabinovich-Fabrikant system which describes physical systems with strong nonlinearity exhibiting unusual behavior.

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Page Count

188

Publisher

CRC Press

Published Date

ISBN 10

1040051685

ISBN 13

9781040051689

Chaos and Complexity Theory for Management: Nonlinear Dynamics

Nonlinear Dynamics

By: Banerjee, Santo

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Chaos and Complexity Theory for Management: Nonlinear Dynamics

Nonlinear Dynamics

By: Banerjee, Santo

Although chaos theory refers to the existence between seemingly random events, it has been gaining the attention of science, technology and managements fields. The shift from traditional procedures to the dynamics of chaos and complexity theory has resulted in a new element of complexity thinking, allowing for a greater capability for analyzing and understanding key business processes. Chaos and Complexity Theory for Management: Nonlinear Dynamics explores chaos and complexity theory and its relationship with the understanding of natural chaos in the business environment. Utilizing these theories aids in comprehending the development of businesses as a complex adaptive system.

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Page Count

449

Publisher

IGI Global

Published Date

ISBN 10

1466625104

ISBN 13

9781466625105

A Route to Chaos Using FPGAs

Volume I: Experimental Observations

By: Bharathwaj Muthuswamy,Santo Banerjee

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A Route to Chaos Using FPGAs

Volume I: Experimental Observations

By: Bharathwaj Muthuswamy,Santo Banerjee

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Page Count

234

Publisher

Springer

Published Date

ISBN 10

331918105X

ISBN 13

9783319181059

Chaotic Dynamics of Fractional Discrete Time Systems

By: Vignesh Dhakshinamoorthy,Guo-Cheng Wu,Santo Banerjee

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Chaotic Dynamics of Fractional Discrete Time Systems

By: Vignesh Dhakshinamoorthy,Guo-Cheng Wu,Santo Banerjee

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Page Count

188

Publisher

CRC Press

Published Date

ISBN 10

1040051685

ISBN 13

9781040051689

Dynamical Systems and Nonlinear Waves in Plasmas

By: Santo Banerjee,Asit Saha

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Dynamical Systems and Nonlinear Waves in Plasmas

By: Santo Banerjee,Asit Saha

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Page Count

207

Publisher

CRC Press

Published Date

ISBN 10

1000404765

ISBN 13

9781000404760

Fractal Functions, Dimensions and Signal Analysis

By: Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar

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Fractal Functions, Dimensions and Signal Analysis

By: Santo Banerjee,D. Easwaramoorthy,A. Gowrisankar

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Solve jigsaw puzzle

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Page Count

132

Publisher

Springer Nature

Published Date

ISBN 10

3030626725

ISBN 13

9783030626723

Book's by Santo Banerjee

Fractal Functions, Dimensions and Signal Analysis

Fractal Functions, Dimensions and Signal Analysis

Introduction to Nonlinear Circuits and Networks

Introduction to Nonlinear Circuits and Networks

Dynamical Systems and Nonlinear Waves in Plasmas

Dynamical Systems and Nonlinear Waves in Plasmas

Fractal Patterns with MATLAB

Fractal Patterns with MATLAB

A Route to Chaos Using FPGAs

A Route to Chaos Using FPGAs

Fractal Patterns in Nonlinear Dynamics and Applications

Fractal Patterns in Nonlinear Dynamics and Applications

Chaotic Dynamics of Fractional Discrete Time Systems

Chaotic Dynamics of Fractional Discrete Time Systems

Chaos and Complexity Theory for Management: Nonlinear Dynamics

Chaos and Complexity Theory for Management: Nonlinear Dynamics

A Route to Chaos Using FPGAs

A Route to Chaos Using FPGAs

Chaotic Dynamics of Fractional Discrete Time Systems

Chaotic Dynamics of Fractional Discrete Time Systems

Dynamical Systems and Nonlinear Waves in Plasmas

Dynamical Systems and Nonlinear Waves in Plasmas

Fractal Functions, Dimensions and Signal Analysis

Fractal Functions, Dimensions and Signal Analysis

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