Elegant Chaos
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Elegant Chaos
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Author : Julien C. Sprott
language : en
Publisher: World Scientific
Release Date : 2010
Elegant Chaos written by Julien C. Sprott and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
1. Fundamentals. 1.1. Dynamical systems. 1.2. State space. 1.3. Dissipation. 1.4. Limit cycles. 1.5. Chaos and strange attractors. 1.6. Poincaré sections and fractals. 1.7. Conservative chaos. 1.8. Two-toruses and quasiperiodicity. 1.9. Largest Lyapunov exponent. 1.10. Lyapunov exponent spectrum. 1.11. Attractor dimension. 1.12. Chaotic transients. 1.13. Intermittency. 1.14. Basins of attraction. 1.15. Numerical methods. 1.16. Elegance -- 2. Periodically forced systems. 2.1. Van der Pol oscillator. 2.2. Rayleigh oscillator. 2.3. Rayleigh oscillator variant. 2.4. Duffing oscillator. 2.5. Quadratic oscillators. 2.6. Piecewise-linear oscillators. 2.7. Signum oscillators. 2.8. Exponential oscillators. 2.9. Other undamped oscillators. 2.10. Velocity forced oscillators. 2.11. Parametric oscillators. 2.12. Complex oscillators -- 3. Autonomous dissipative systems. 3.1. Lorenz system. 3.2. Diffusionless Lorenz system. 3.3. Rs̈sler system. 3.4. Other quadratic systems. 3.5. Jerk systems. 3.6. Circulant systems. 3.7. Other systems -- 4. Autonomous Conservative Systems. 4.1. Nosé-Hoover oscillator. 4.2. Nosé-Hoover variants. 4.3. Jerk systems. 4.4. Circulant systems -- 5. Low-dimension systems (D3). 5.1. Dixon system. 5.2. Dixon variants. 5.3. Logarithmic case. 5.4. Other cases -- 6. High-dimensional systems (D3). 6.1. Periodically forced systems. 6.2. Master-slave oscillators. 6.3. Mutually coupled nonlinear oscillators. 6.4. Hamiltonian systems. 6.5. Anti-Newtonian systems. 6.6. Hyperjerk systems. 6.7. Hyperchaotic systems. 6.8. Autonomous complex systems. 6.9. Lotka-Volterra systems. 6.10. Artificial neural networks -- 7. Circulant systems. 7.1. Lorenz-Emanuel system. 7.2. Lotka-Volterra systems. 7.3. Antisymmetric quadratic system. 7.4. Quadratic ring system. 7.5. Cubic ring system. 7.6. Hyperlabyrinth system. 7.7. Circulant neural networks. 7.8. Hyperviscous ring. 7.9. Rings of oscillators. 7.10. Star systems -- 8. Spatiotemporal systems. 8.1. Numerical methods. 8.2. Kuramoto-Sivashinsky equation. 8.3. Kuramoto-Sivashinsky variants. 8.4. Chaotic traveling waves. 8.5. Continuum ring systems. 8.6. Traveling wave variants -- 9. Time-delay systems. 9.1. Delay differential equations. 9.2. Mackey-Glass equation. 9.3. Ikeda DDE. 9.4. Sinusoidal DDE. 9.5. Polynomial DDE. 9.6. Sigmoidal DDE. 9.7. Signum DDE. 9.8. Piecewise-linear DDEs. 9.9. Asymmetric logistic DDE with continuous delay -- 10. Chaotic electrical circuits. 10.1. Circuit elegance. 10.2. Forced relaxation oscillator. 10.3. Autonomous relaxation oscillator. 10.4. Coupled relaxation oscillators. 10.5. Forced diode resonator. 10.6. Saturating inductor circuit. 10.7. Forced piecewise-linear circuit. 10.8. Chua's circuit. 10.9. Nishio's circuit. 10.10. Wien-bridge oscillator. 10.11. Jerk circuits. 10.12. Master-slave oscillator. 10.13. Ring of oscillators. 10.14. Delay-line oscillator
Elegant Fractals Automated Generation Of Computer Art
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Author : Julien Clinton Sprott
language : en
Publisher: World Scientific Publishing
Release Date : 2018-10-04
Elegant Fractals Automated Generation Of Computer Art written by Julien Clinton Sprott and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Computers categories.
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).
Elegant Circuits Simple Chaotic Oscillators
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Author : Julien Clinton Sprott
language : en
Publisher: World Scientific
Release Date : 2021-12-17
Elegant Circuits Simple Chaotic Oscillators written by Julien Clinton Sprott and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-17 with Science categories.
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 Automation Robotic Analysis Of Chaotic Systems
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Author : Julien Clinton Sprott
language : en
Publisher: World Scientific
Release Date : 2023-04-14
Elegant Automation Robotic Analysis Of Chaotic Systems written by Julien Clinton Sprott and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-14 with Science categories.
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.
Elegant Simulations From Simple Oscillators To Many Body Systems
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Author : Julien Clinton Sprott
language : en
Publisher: World Scientific
Release Date : 2022-12-20
Elegant Simulations From Simple Oscillators To Many Body Systems written by Julien Clinton Sprott and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-20 with Science categories.
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.
Nothing Is Beyond Our Reach
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Author : Kristie Macrakis
language : en
Publisher: Georgetown University Press
Release Date : 2023
Nothing Is Beyond Our Reach written by Kristie Macrakis and has been published by Georgetown University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Computers categories.
"Ever since the earliest days of the Cold War, American intelligence agencies have launched spies in the sky, implanted spies in the ether, burrowed spies underground, sunk spies in the ocean, and even tried chemical means to pry open the human mind. The United States increasingly has covered the globe with planes, satellites, drones, electronics, tunnels, and submarines all in the service of intelligence. Hard targets meant that American intelligence could not entirely rely on human spies, but it was more than that. Nothing is Beyond Our Reach reveals how America's love-affair with technology has led to its dependence on machines in intelligence collection and how this has almost inadvertently created a global surveillance empire. In a lively and engaging narrative, author Kristie Macrakis tells this story of how intelligence has changed from American technophilia and what its implications will be"--
Introduction To Mathematical Modeling And Chaotic Dynamics
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Author : Ranjit Kumar Upadhyay
language : en
Publisher: CRC Press
Release Date : 2013-07-23
Introduction To Mathematical Modeling And Chaotic Dynamics written by Ranjit Kumar Upadhyay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-23 with Mathematics categories.
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.
Advanced Mathematics For The Modeling And Solution Of Challenging Problems In Engineering
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Author : Oscar Castillo
language : en
Publisher: Springer Nature
Release Date : 2025-06-01
Advanced Mathematics For The Modeling And Solution Of Challenging Problems In Engineering written by Oscar Castillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-01 with Technology & Engineering categories.
This book includes studies that give mathematical solution methods and mathematical modeling to support these methods for solving problems in the current application area of engineering, as well as studies that include solutions for problems that are also related to current life areas. In this book, some current problems in the field of mathematics and engineering, solutions to solve these problems and existing engineering methods for these problems are included. Basically, machinery, chemistry, electronics, computers, construction, environment, etc. studies in both the application and theoretical fields of mathematics are needed to solve optimization, modeling, encryption methods and thermal problems that are currently encountered in engineering fields. In this book, some current problems are presented and related theoretical and applied mathematical studies are included.
Advances And Applications In Chaotic Systems
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Author : Sundarapandian Vaidyanathan
language : en
Publisher: Springer
Release Date : 2016-03-22
Advances And Applications In Chaotic Systems written by Sundarapandian Vaidyanathan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-22 with Technology & Engineering categories.
This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.
Control Of Imperfect Nonlinear Electromechanical Large Scale Systems From Dynamics To Hardware Implementation
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Author : Luigi Fortuna
language : en
Publisher: World Scientific
Release Date : 2017-05-19
Control Of Imperfect Nonlinear Electromechanical Large Scale Systems From Dynamics To Hardware Implementation written by Luigi Fortuna and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-19 with Computers categories.
This book focuses on a class of uncertain systems that are called imperfect, and shows how much systems can regularly work if an appropriate control strategy is adopted. Along with some practical well studied examples, a formalization of the models for imperfect system is considered and a control strategy is proposed. Experimental case studies on electromechanical systems are also included.New concepts, experimental innovative circuits and laboratory details allow the reader to implement at low cost the outlined strategy. Emergent topics in nonlinear device realization are emphasized with the aim to allow researchers and students to perform experiments with large scale electromechanical systems. Moreover, the possibility of using imperfections and noise to generate nonlinear strange behavior is discussed.