Miguel A. F. Sanjuan - Böcker

This book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observations, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, in astronomy it is uncommon to have the possibility of altering the key parameters of the studied objects. Therefore, the numerical simulations offer an essential tool for analysing these systems, and their reliability is of ever-increasing interest and importance. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation.This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the strong sensitivity to initial conditions and the use of Lyapunov exponents to characterize this sensitivity. This method is illustrated using several well-known continuous dynamical systems, such as the Contopoulos, Hénon-Heiles and Rössler systems. This second edition revises and significantly enlarges the material of the first edition by providing new entry points for discussing new predictability issues on a variety of areas such as machine decision-making, partial differential equations or the analysis of attractors and basins. Finally, the parts of the book devoted to the application of these ideas to astronomy have been greatly enlarged, by first presenting some basics aspects of predictability in astronomy and then by expanding these ideas to a detailed analysis of a galactic potential.

This book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observations, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, in astronomy it is uncommon to have the possibility of altering the key parameters of the studied objects. Therefore, the numerical simulations offer an essential tool for analysing these systems, and their reliability is of ever-increasing interest and importance. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation.This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the strong sensitivity to initial conditions and the use of Lyapunov exponents to characterize this sensitivity. This method is illustrated using several well-known continuous dynamical systems, such as the Contopoulos, Hénon-Heiles and Rössler systems. This second edition revises and significantly enlarges the material of the first edition by providing new entry points for discussing new predictability issues on a variety of areas such as machine decision-making, partial differential equations or the analysis of attractors and basins. Finally, the parts of the book devoted to the application of these ideas to astronomy have been greatly enlarged, by first presenting some basics aspects of predictability in astronomy and then by expanding these ideas to a detailed analysis of a galactic potential.

This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years.Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.

The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics.The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering.As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years.Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.

This book is primarily concerned with the computational aspects of predictability of dynamical systems – in particular those where observation, modeling and computation are strongly interdependent.

The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics.The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering.As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

Demonstrating many fundamental concepts of physics and engineering through the working principles of popular science toys is inexpensive, quickly reaching the senses and inspiring a better learning. The systematic way of setting theoretical model equations for the toys provides a remarkable experience in constructing model equations for physical and engineering systems.Given that most science toys are based on the principles of physics, and to cater to the needs of graduate and master-level programme students in physics and engineering, the present book covers more than 40 wide ranging popular toys. For each toy various features are presented including history, construction, working principle, theoretical model, a solved problem and 5-10 exercises.A course on The Physics of Toys can be designed based on the proposed book to be taught as a full course at graduate and master-level and even to students who have never been exposed to physics. Further, the features of the toys covered in this book can be used to illustrate various concepts and principles in different branches of physics and engineering.

Demonstrating many fundamental concepts of physics and engineering through the working principles of popular science toys is inexpensive, quickly reaching the senses and inspiring a better learning. The systematic way of setting theoretical model equations for the toys provides a remarkable experience in constructing model equations for physical and engineering systems.Given that most science toys are based on the principles of physics, and to cater to the needs of graduate and master-level programme students in physics and engineering, the present book covers more than 40 wide ranging popular toys. For each toy various features are presented including history, construction, working principle, theoretical model, a solved problem and 5-10 exercises.A course on The Physics of Toys can be designed based on the proposed book to be taught as a full course at graduate and master-level and even to students who have never been exposed to physics. Further, the features of the toys covered in this book can be used to illustrate various concepts and principles in different branches of physics and engineering.

This review volume consists an indispensable collection of research papers chronicling the recent progress in controlling chaos. Here, new theoretical ideas, as experimental implementations of controlling chaos, are included, while the applications contained in this volume can be referred to as turbulent magnetized plasmas, chaotic neural networks, modeling city traffic and models of interest in celestial mechanics.Recent Progress in Controlling Chaos provides an excellent broad overview of the subject matter, and will be especially useful for graduate students, researchers and scientists working in the areas of nonlinear dynamics, chaos and complex systems. The authors, world-renowned scientists and prominent experts in the field of controlling chaos, will offer readers through their research works, a fascinating insight into the state-of-the-art technology used in the progress in key techniques and concepts in the field of control.

This book presents various types of aperiodic resonances in the form of a complete theoretical framework for the first time. It makes aperiodic resonance be a new disciplinary direction. In addition to the achievements in existing papers, the book proposes some new methods and discovers some new phenomena about different aperiodic resonances in nonlinear systems. The book includes theoretical analysis methods and their applications in three typical engineering backgrounds. It links theoretical researches on physical phenomena with different engineering problems. It aims to solve engineering problems from a new perspective based on aperiodic resonance theories.