Chaotic Systems With Multistability And Hidden Attractors
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Chaotic Systems With Multistability And Hidden Attractors
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Author : Xiong Wang
language : en
Publisher: Springer Nature
Release Date : 2021-12-01
Chaotic Systems With Multistability And Hidden Attractors written by Xiong Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-01 with Technology & Engineering categories.
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.
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
Dynamical Systems
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Author : René Lozi
language : en
Publisher: CRC Press
Release Date : 2025-06-23
Dynamical Systems written by René Lozi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-23 with Mathematics categories.
This book offers a captivating exploration of the intersection between mathematics, chaos theory, and dynamical systems through the personal journeys of twelve renowned mathematicians and physicists from China, Europe, Russia, and the USA. The first section of the book provides an intimate look into the formative experiences and early steps of these scientists. In these life stories, the names of other famous mathematicians arise, crisscrossing all the stories in unexpected ways. The second part of the book explores the practical applications of chaotic attractors in various fields. These include chaos-based encryption in cryptography, sensor and actuator placement in Chua circuits for control systems, and chaotic dynamics in remote sensing for crop modeling. It also highlights the role of chaos theory in the development of memristors following Leon Chua’s 1971 discovery, leading to advances in nonlinear dynamics, hyperchaos, and memristor-based systems. The chapters further examine how chaos theory addresses modern challenges such as modeling COVID-19 spread using SEIR models and optimizing mobile network design, demonstrating the wide-reaching impact of chaotic systems in real-world applications. This book will be of great value to students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications. This book includes a revised introduction and a new chapter. The remaining chapters were originally published in Journal of Difference Equations and Applications.
Attractor Dimension Estimates For Dynamical Systems Theory And Computation
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Author : Nikolay Kuznetsov
language : en
Publisher: Springer Nature
Release Date : 2020-07-02
Attractor Dimension Estimates For Dynamical Systems Theory And Computation written by Nikolay Kuznetsov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-02 with Computers categories.
This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.
Recent Advances In Chaotic Systems And Synchronization
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Author : Olfa Boubaker
language : en
Publisher: Academic Press
Release Date : 2018-11-05
Recent Advances In Chaotic Systems And Synchronization written by Olfa Boubaker and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Computers categories.
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
Nonlinear Dynamical Systems With Self Excited And Hidden Attractors
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Author : Viet-Thanh Pham
language : en
Publisher: Springer
Release Date : 2018-02-26
Nonlinear Dynamical Systems With Self Excited And Hidden Attractors written by Viet-Thanh Pham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-26 with Technology & Engineering categories.
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.
New Perspectives On Nonlinear Dynamics And Complexity
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Author : Dimitri Volchenkov
language : en
Publisher: Springer Nature
Release Date : 2022-07-29
New Perspectives On Nonlinear Dynamics And Complexity written by Dimitri Volchenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-29 with Technology & Engineering categories.
This book presents select, recent developments in nonlinear and complex systems reported at the 1st Online Conference on Nonlinear Dynamics and Complexity, held on November 23-25, 2020. It provides an exchange recent developments, discoveries, and progresses in Nonlinear Dynamics and Complexity. The collection presents fundamental and frontier theories and techniques for modern science and technology, stimulates more research interest for exploration of nonlinear science and complexity; and passes along new knowledge and insight to the next generation of engineers and technologists in a range of fields.
Nonlinear Dynamics And Entropy Of Complex Systems With Hidden And Self Excited Attractors
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Author : Christos Volos
language : en
Publisher: MDPI
Release Date : 2019-05-03
Nonlinear Dynamics And Entropy Of Complex Systems With Hidden And Self Excited Attractors written by Christos Volos and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-03 with Technology & Engineering categories.
In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
Mobile Robot Motion Control And Path Planning
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Author : Ahmad Taher Azar
language : en
Publisher: Springer Nature
Release Date : 2023-06-30
Mobile Robot Motion Control And Path Planning written by Ahmad Taher Azar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-30 with Technology & Engineering categories.
This book presents the recent research advances in linear and nonlinear control techniques. From both a theoretical and practical standpoint, motion planning and related control challenges are key parts of robotics. Indeed, the literature on the planning of geometric paths and the generation of time-based trajectories, while accounting for the compatibility of such paths and trajectories with the kinematic and dynamic constraints of a manipulator or a mobile vehicle, is extensive and rich in historical references. Path planning is vital and critical for many different types of robotics, including autonomous vehicles, multiple robots, and robot arms. In the case of multiple robot route planning, it is critical to produce a safe path that avoids colliding with objects or other robots. When designing a safe path for an aerial or underwater robot, the 3D environment must be considered. As the number of degrees of freedom on a robot arm increases, so does the difficulty of path planning. As a result, safe pathways for high-dimensional systems must be developed in a timely manner. Nonetheless, modern robotic applications, particularly those requiring one or more robots to operate in a dynamic environment (e.g., human–robot collaboration and physical interaction, surveillance, or exploration of unknown spaces with mobile agents, etc.), pose new and exciting challenges to researchers and practitioners. For instance, planning a robot's motion in a dynamic environment necessitates the real-time and online execution of difficult computational operations. The development of efficient solutions for such real-time computations, which could be offered by specially designed computational architectures, optimized algorithms, and other unique contributions, is thus a critical step in the advancement of present and future-oriented robotics.
Backstepping Control Of Nonlinear Dynamical Systems
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Author : Sundarapandian Vaidyanathan
language : en
Publisher: Academic Press
Release Date : 2020-08-15
Backstepping Control Of Nonlinear Dynamical Systems written by Sundarapandian Vaidyanathan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-15 with Technology & Engineering categories.
Backstepping Control of Nonlinear Dynamical Systems addresses both the fundamentals of backstepping control and advances in the field. The latest techniques explored include 'active backstepping control', 'adaptive backstepping control', 'fuzzy backstepping control' and 'adaptive fuzzy backstepping control'. The reference book provides numerous simulations using MATLAB and circuit design. These illustrate the main results of theory and applications of backstepping control of nonlinear control systems. Backstepping control encompasses varied aspects of mechanical engineering and has many different applications within the field. For example, the book covers aspects related to robot manipulators, aircraft flight control systems, power systems, mechanical systems, biological systems and chaotic systems. This multifaceted view of subject areas means that this useful reference resource will be ideal for a large cross section of the mechanical engineering community. - Details the real-world applications of backstepping control - Gives an up-to-date insight into the theory, uses and application of backstepping control - Bridges the gaps for different fields of engineering, including mechanical engineering, aeronautical engineering, electrical engineering, communications engineering, robotics and biomedical instrumentation