Elegant Circuits Simple Chaotic Oscillators

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Elegant Circuits: Simple Chaotic Oscillators

Author : Julien Clinton Sprott
Publisher : World Scientific
ISBN 13 : 9811240019
Total Pages : 357 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Elegant Circuits: Simple Chaotic Oscillators by : Julien Clinton Sprott

Download or read book Elegant Circuits: Simple Chaotic Oscillators written by Julien Clinton Sprott and published by World Scientific. This book was released on 2021-12-17 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos is the study of the underlying determinism in the seemingly random phenomena that occur all around us. One of the best experimental demonstrations of chaos occurs in electrical circuits when the parameters are chosen carefully. We will show you how to construct such chaotic circuits for use in your own studies and demonstrations while teaching you the basics of chaos.This book should be of interest to researchers and hobbyists looking for a simple way to produce a chaotic signal. It should also be useful to students and their instructors as an engaging way to learn about chaotic dynamics and electronic circuits. The book assumes only an elementary knowledge of calculus and the ability to understand a schematic diagram and the components that it contains.You will get the most out of this book if you can construct the circuits for yourself. There is no substitute for the thrill and insight of seeing the output of a circuit you built unfold as the trajectory wanders in real time across your oscilloscope screen. A goal of this book is to inspire and delight as well as to teach.

Elegant Chaos: Algebraically Simple Chaotic Flows

Author : Julien Clinton Sprott
Publisher : World Scientific
ISBN 13 : 9814468673
Total Pages : 302 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Elegant Chaos: Algebraically Simple Chaotic Flows by : Julien Clinton Sprott

Download or read book Elegant Chaos: Algebraically Simple Chaotic Flows written by Julien Clinton Sprott and published by World Scientific. This book was released on 2010-03-22 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos.No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.

Elegant Simulations: From Simple Oscillators To Many-body Systems

Author : Julien Clinton Sprott
Publisher : World Scientific
ISBN 13 : 9811263582
Total Pages : 325 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Elegant Simulations: From Simple Oscillators To Many-body Systems by : Julien Clinton Sprott

Download or read book Elegant Simulations: From Simple Oscillators To Many-body Systems written by Julien Clinton Sprott and published by World Scientific. This book was released on 2022-12-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: A recent development is the discovery that simple systems of equations can have chaotic solutions in which small changes in initial conditions have a large effect on the outcome, rendering the corresponding experiments effectively irreproducible and unpredictable. An earlier book in this sequence, Elegant Chaos: Algebraically Simple Chaotic Flows provided several hundred examples of such systems, nearly all of which are purely mathematical without any obvious connection with actual physical processes and with very limited discussion and analysis.In this book, we focus on a much smaller subset of such models, chosen because they simulate some common or important physical phenomenon, usually involving the motion of a limited number of point-like particles, and we discuss these models in much greater detail. As with the earlier book, the chosen models are the mathematically simplest formulations that exhibit the phenomena of interest, and thus they are what we consider 'elegant.'Elegant models, stripped of unnecessary detail while maximizing clarity, beauty, and simplicity, occupy common ground bordering both real-world modeling and aesthetic mathematical analyses. A computational search led one of us (JCS) to the same set of differential equations previously used by the other (WGH) to connect the classical dynamics of Newton and Hamilton to macroscopic thermodynamics. This joint book displays and explores dozens of such relatively simple models meeting the criteria of elegance, taste, and beauty in structure, style, and consequence.This book should be of interest to students and researchers who enjoy simulating and studying complex particle motions with unusual dynamical behaviors. The book assumes only an elementary knowledge of calculus. The systems are initial-value iterated maps and ordinary differential equations but they must be solved numerically. Thus for readers a formal differential equations course is not at all necessary, of little value and limited use.

Elegant Fractals: Automated Generation Of Computer Art

Author : Julien Clinton Sprott
Publisher : World Scientific Publishing
ISBN 13 : 9813237155
Total Pages : 266 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Elegant Fractals: Automated Generation Of Computer Art by : Julien Clinton Sprott

Download or read book Elegant Fractals: Automated Generation Of Computer Art written by Julien Clinton Sprott and published by World Scientific Publishing. This book was released on 2018-10-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractals are intricate geometrical forms that contain miniature copies of themselves on ever smaller scales. This colorful book describes methods for producing an endless variety of fractal art using a computer program that searches through millions of equations looking for those few that can produce images having aesthetic appeal. Over a hundred examples of such images are included with a link to the software that produced these images, and can also produce many more similar fractals. The underlying mathematics of the process is also explained in detail.Other books by the author that could be of interest to the reader are Elegant Chaos: Algebraically Simple Chaotic Flows (J C Sprott, 2010) and Elegant Circuits: Simple Chaotic Oscillators (J C Sprott and W J Thio, 2020).

Chaos in Nonlinear Oscillators

Author : Muthusamy Lakshmanan
Publisher : World Scientific
ISBN 13 : 9789810221430
Total Pages : 346 pages
Book Rating : 4.2/5 (214 download)

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Book Synopsis Chaos in Nonlinear Oscillators by : Muthusamy Lakshmanan

Download or read book Chaos in Nonlinear Oscillators written by Muthusamy Lakshmanan and published by World Scientific. This book was released on 1996 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.

Nonlinear Dynamics in Circuits

Author : Thomas L. Carroll
Publisher : World Scientific
ISBN 13 : 9789810224387
Total Pages : 352 pages
Book Rating : 4.2/5 (243 download)

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Book Synopsis Nonlinear Dynamics in Circuits by : Thomas L. Carroll

Download or read book Nonlinear Dynamics in Circuits written by Thomas L. Carroll and published by World Scientific. This book was released on 1995 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes the use of simple analog circuits to study nonlinear dynamics, chaos and stochastic resonance. The circuit experiments that are described are mostly easy and inexpensive to reproduce, and yet these experiments come from the forefront of nonlinear dynamics research. The individual chapters describe why analog circuits are so useful for studying nonlinear dynamics, and include theoretical as well as experimental results from some of the leading researchers in the field. Most of the articles contain some tutorial sections for the less experienced readers.The audience for this book includes researchers in nonlinear dynamics, chaos and statistical physics as well as electrical engineering, and graduate and advanced undergraduate students in these fields.

A Gallery of Chua Attractors

Author : Eleonora Bilotta
Publisher : World Scientific
ISBN 13 : 9812790624
Total Pages : 607 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis A Gallery of Chua Attractors by : Eleonora Bilotta

Download or read book A Gallery of Chua Attractors written by Eleonora Bilotta and published by World Scientific. This book was released on 2008 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos is considered as one of the most important concepts in modern science. It originally appeared only in computer simulation (the famous Lorenz equation of 1963), but this changed with the introduction of Chua's oscillator (1986) — a simple electronic circuit with the ability to generate a vast range of chaotic behaviors. With Chua's circuit, chaos became a physical phenomenon, readily understood and represented in mathematical language. Yet, even so, it is still difficult for the non-specialist to appreciate the full variety of behaviors that the system can produce.This book aims to bridge the gap. A gallery of nearly 900 “chaotic attractors” — some generated by Chua's physical circuit, the majority through computer simulation of the circuit and its generalizations — are illustrated as 3D color images, time series and fast Fourier transform algorithms. For interested researchers, also presented is the information necessary to replicate the behaviors and images. Finally, how the fractal richness can be plied to artistic ends in generating music and interesting sounds is shown; some examples are included in the DVD-ROM which comes with the book.The contents have also appeared in the International Journal of Bifurcation and Chaos (2007).

Recent Advances in Chaotic Systems and Synchronization

Author : Olfa Boubaker
Publisher : Academic Press
ISBN 13 : 012816266X
Total Pages : 394 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Recent Advances in Chaotic Systems and Synchronization by : Olfa Boubaker

Download or read book Recent Advances in Chaotic Systems and Synchronization written by Olfa Boubaker and published by Academic Press. This book was released on 2018-11-05 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications is a major reference for scientists and engineers interested in applying new computational and mathematical tools for solving complex problems related to modeling, analyzing and synchronizing chaotic systems. Furthermore, it offers an array of new, real-world applications in the field. Written by eminent scientists in the field of control theory and nonlinear systems from 19 countries (Cameroon, China, Ethiopia, France, Greece, India, Italia, Iran, Japan, Mexico, and more), this book covers the latest advances in chaos theory, along with the efficiency of novel synchronization approaches. Readers will find the fundamentals and algorithms related to the analysis and synchronization of chaotic systems, along with key applications, including electronic design, text and image encryption, and robot control and tracking. - Explores and evaluates the latest real-world applications of chaos across various engineering and biomedical engineering fields - Investigates advances in chaos synchronization techniques, including the continuous sliding-mode control approach, hybrid synchronization between chaotic and hyperchaotic systems, and neural network synchronization - Presents recent advances in chaotic systems through an overview of new systems and new proprieties

Elegant Automation: Robotic Analysis Of Chaotic Systems

Author : Julien Clinton Sprott
Publisher : World Scientific
ISBN 13 : 9811277532
Total Pages : 348 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Elegant Automation: Robotic Analysis Of Chaotic Systems by : Julien Clinton Sprott

Download or read book Elegant Automation: Robotic Analysis Of Chaotic Systems written by Julien Clinton Sprott and published by World Scientific. This book was released on 2023-04-14 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was mostly written by a machine that was programmed to search a system of equations for chaotic solutions, simplify the equations to the extent possible, analyze the behavior, produce figures, and write the accompanying text. The equations are coupled autonomous ordinary differential equations with three variables and at least one nonlinearity. Fifty simple systems are included. Some are old and familiar; others are relatively new and unknown. They are chosen to illustrate by simple example most of dynamical behaviors that can occur in low-dimensional chaotic systems.There is no substitute for the thrill and insight of seeing the solution of a simple equation unfold as the trajectory wanders in real time across your computer screen using a program of your own making. A goal of this book is to inspire and delight as well as to teach. It provides a wealth of examples ripe for further study and extension, and it offers a glimpse of a future when artificial intelligence supplants many of the mundane tasks that accompany dynamical systems research and becomes a true and tireless collaborator.

Handbook of Research on Modeling, Analysis, and Control of Complex Systems

Author : Azar, Ahmad Taher
Publisher : IGI Global
ISBN 13 : 1799857905
Total Pages : 685 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Handbook of Research on Modeling, Analysis, and Control of Complex Systems by : Azar, Ahmad Taher

Download or read book Handbook of Research on Modeling, Analysis, and Control of Complex Systems written by Azar, Ahmad Taher and published by IGI Global. This book was released on 2020-12-05 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current literature on dynamic systems is quite comprehensive, and system theory’s mathematical jargon can remain quite complicated. Thus, there is a need for a compendium of accessible research that involves the broad range of fields that dynamic systems can cover, including engineering, life sciences, and the environment, and which can connect researchers in these fields. The Handbook of Research on Modeling, Analysis, and Control of Complex Systems is a comprehensive reference book that describes the recent developments in a wide range of areas including the modeling, analysis, and control of dynamic systems, as well as explores related applications. The book acts as a forum for researchers seeking to understand the latest theory findings and software problem experiments. Covering topics that include chaotic maps, predictive modeling, random bit generation, and software bug prediction, this book is ideal for professionals, academicians, researchers, and students in the fields of electrical engineering, computer science, control engineering, robotics, power systems, and biomedical engineering.

Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors

Author : Viet-Thanh Pham
Publisher : Springer
ISBN 13 : 3319712438
Total Pages : 497 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors by : Viet-Thanh Pham

Download or read book Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors written by Viet-Thanh Pham and published by Springer. This book was released on 2018-02-26 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with self-excited and hidden attractors. The book includes 20 chapters contributed by respected experts, which focus on various applications such as biological systems, memristor-based systems, fractional-order systems, finance systems, business cycles, oscillators, coupled systems, hyperchaotic systems, flexible robot manipulators, electronic circuits, and control models. Special attention is given to modeling, design, circuit realization, and practical applications to address recent research problems in nonlinear dynamical systems. The book provides a valuable reference guide to nonlinear dynamical systems for engineers, researchers, and graduate students, especially those whose work involves mechanics, electrical engineering, and control systems.

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.

Synchronization in Networks of Nonlinear Circuits

Author : Mattia Frasca
Publisher : Springer
ISBN 13 : 3319759574
Total Pages : 115 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Synchronization in Networks of Nonlinear Circuits by : Mattia Frasca

Download or read book Synchronization in Networks of Nonlinear Circuits written by Mattia Frasca and published by Springer. This book was released on 2018-03-10 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses synchronization in networks of coupled systems. It illustrates the main aspects of the phenomenon through concise theoretical results and code, allowing readers to reproduce them and encouraging readers to pursue their own experimentation. The book begins by introducing the mathematical representation of nonlinear circuits and the code for their simulation. This is followed by a brief account of the concept of the complex network, which describes the main aspects of complex networks and the main model types, with a particular focus on the code used to study and reproduce the models. The focus then shifts to the process through which independent nonlinear circuits that follow different trajectories without coupling share some properties of their motion: synchronization. The authors present the main techniques for studying synchronization in complex networks, including the major measures, the stability properties and control techniques. The book then moves on to advanced topics in synchronization of complex networks by examining forms of synchronization in which not all the units share the same trajectory, namely chimera states, clustering synchronization, and relay and remote synchronization. Simple codes for experimentation with these topics and control methods are also provided. In closing, the book addresses the problem of synchronization in time-varying networks.

Chaos Theory Tamed

Author : Garnett Williams
Publisher : CRC Press
ISBN 13 : 1482295415
Total Pages : 518 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Chaos Theory Tamed by : Garnett Williams

Download or read book Chaos Theory Tamed written by Garnett Williams and published by CRC Press. This book was released on 1997-09-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.

Fractional Order Systems

Author : Ahmad Taher Azar
Publisher : Academic Press
ISBN 13 : 0128163089
Total Pages : 746 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Fractional Order Systems by : Ahmad Taher Azar

Download or read book Fractional Order Systems written by Ahmad Taher Azar and published by Academic Press. This book was released on 2018-08-16 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas such as control engineering, electrical engineering, mechanical engineering, computer science, and information technology will find the book most informative. - Discusses multi-disciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results - Includes new circuits and systems based on the new nonlinear elements - Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers - Closes the gap between theoretical approaches and real-world applications - Provides MATLAB® and Simulink code for many of the applications in the book

Introduction to Mathematical Modeling and Chaotic Dynamics

Author : Ranjit Kumar Upadhyay
Publisher : CRC Press
ISBN 13 : 1439898871
Total Pages : 363 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Introduction to Mathematical Modeling and Chaotic Dynamics by : Ranjit Kumar Upadhyay

Download or read book Introduction to Mathematical Modeling and Chaotic Dynamics written by Ranjit Kumar Upadhyay and published by CRC Press. This book was released on 2013-07-23 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB®. The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural science, focusing on one- and two-dimensional continuous and discrete time models. Moving on to chaotic dynamics, the authors discuss ways to study chaos, types of chaos, and methods for detecting chaos. They also explore chaotic dynamics in single and multiple species systems. The text concludes with a brief discussion on models of mechanical systems and electronic circuits. Suitable for advanced undergraduate and graduate students, this book provides a practical understanding of how the models are used in current natural science and engineering applications. Along with a variety of exercises and solved examples, the text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

Rhythms of the Brain

Author : G. Buzsáki
Publisher : Oxford University Press
ISBN 13 : 0199828237
Total Pages : 465 pages
Book Rating : 4.1/5 (998 download)

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Book Synopsis Rhythms of the Brain by : G. Buzsáki

Download or read book Rhythms of the Brain written by G. Buzsáki and published by Oxford University Press. This book was released on 2011 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of mechanisms in the brain that allow complicated things to happen in a coordinated fashion have produced some of the most spectacular discoveries in neuroscience. This book provides eloquent support for the idea that spontaneous neuron activity, far from being mere noise, is actually the source of our cognitive abilities. It takes a fresh look at the coevolution of structure and function in the mammalian brain, illustrating how self-emerged oscillatory timing is the brain's fundamental organizer of neuronal information. The small-world-like connectivity of the cerebral cortex allows for global computation on multiple spatial and temporal scales. The perpetual interactions among the multiple network oscillators keep cortical systems in a highly sensitive "metastable" state and provide energy-efficient synchronizing mechanisms via weak links. In a sequence of "cycles," György Buzsáki guides the reader from the physics of oscillations through neuronal assembly organization to complex cognitive processing and memory storage. His clear, fluid writing-accessible to any reader with some scientific knowledge-is supplemented by extensive footnotes and references that make it just as gratifying and instructive a read for the specialist. The coherent view of a single author who has been at the forefront of research in this exciting field, this volume is essential reading for anyone interested in our rapidly evolving understanding of the brain.