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Chaotic Flows

Author: Oleg G. Bakunin

Publisher: Springer Science & Business Media

Published: 2011-08-29

Total Pages: 349

ISBN-13: 3642203507

The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.

Elegant Chaos: Algebraically Simple Chaotic Flows

Author: Julien Clinton Sprott

Publisher: World Scientific

Published: 2010-03-22

Total Pages: 302

ISBN-13: 9814468673

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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.

Single and Two-Phase Flows on Chemical and Biomedical Engineering

Author: Ricardo Dias

Publisher: Bentham Science Publishers

Published: 2012-07-30

Total Pages: 667

ISBN-13: 1608052958

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Single and two-phase flows are ubiquitous in most natural process and engineering systems. Examples of systems or process include, packed bed reactors, either single phase or multiphase, absorber and adsorber separation columns, filter beds, plate heat exchangers, flow of viscoelastic fluids in polymer systems, or the enhanced recovery of oil, among others. In each case the flow plays a central role in determining the system or process behavior and performance. A better understanding of the underlying physical phenomena and the ability to describe the phenomena properly are both crucial to improving design, operation and control processes involving the flow of fluids, ensuring that they will be more efficient and cost effective. Expanding disciplines such as microfluidics and the simulation of complex flow physical systems, such as blood flow in physiological networks, also rely heavily on accurate predictions of fluid flow. Recent advances either in computational and experimental techniques are improving the existing knowledge of single and multiphase flows in engineering and physical systems of interest. This ebook is a review on the state-of-the-art and recent advances in critical areas of fluid mechanics and transport phenomena with respect to chemical and biomedical engineering applications.

Recent Advances in Chaotic Systems and Synchronization

Author: Olfa Boubaker

Publisher: Academic Press

Published: 2018-11-05

Total Pages: 391

ISBN-13: 012816266X

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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

Chaotic Systems with Multistability and Hidden Attractors

Author: Xiong Wang

Publisher: Springer Nature

Published: 2021-12-01

Total Pages: 661

ISBN-13: 3030758214

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This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.

Recent Trends In Chaotic, Nonlinear And Complex Dynamics

Author: Jan Awrejcewicz

Publisher: World Scientific

Published: 2021-07-26

Total Pages: 561

ISBN-13: 981122191X

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In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.

Classical Mechanics

Author: Joseph L. McCauley

Publisher: Cambridge University Press

Published: 1997-05-08

Total Pages: 492

ISBN-13: 9780521578820

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This advanced text is the first book to describe the subject of classical mechanics in the context of the language and methods of modern nonlinear dynamics. The organizing principle of the text is integrability vs. nonintegrability.

Advances and Applications in Chaotic Systems

Author: Sundarapandian Vaidyanathan

Publisher: Springer

Published: 2016-03-22

Total Pages: 599

ISBN-13: 3319302795

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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.

Elegant Chaos

Author: Julien C. Sprott

Publisher: World Scientific

Published: 2010

Total Pages: 302

ISBN-13: 9812838821

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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

The Kinematics of Mixing

Author: J. M. Ottino

Publisher: Cambridge University Press

Published: 1989

Total Pages: 390

ISBN-13: 9780521368780

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In spite of its universality, mixing is poorly understood and generally speaking, mixing problems are attacked on a case-by-case basis. This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint. The author's aim is to provide a conceptually clear basis from which to launch analysis and to facilitate an understanding of the numerous mixing problems encountered in nature and technology. After presenting the necessary background in kinematics and fluid dynamics, Professor Ottino considers various examples of dealing with necessary background in dynamical systems and chaos. The book assumes little previous knowledge of fluid dynamics and dynamical systems and can be used as a textbook by final-year undergraduates, graduate students and researchers in applied mathematics, engineering science, geophysics and physics who have an interest in fluid dynamics, continuum mechanics and dynamical systems. It is profusely illustrated in colour, with many line diagrams and half-tones. Systems which illustrate the most important concepts, many exercises and examples are included.