Stability Structures And Chaos In Nonlinear Synchronization Networks
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Stability Structures And Chaos In Nonlinear Synchronization Networks
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Author : Valentin S Afraimovich
language : en
Publisher: World Scientific
Release Date : 1995-01-16
Stability Structures And Chaos In Nonlinear Synchronization Networks written by Valentin S Afraimovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-16 with Science categories.
The understanding of fields and media using discrete lattice models has been greatly aided by the advent of powerful computers. This has also led to the formulation of new and inspiring problems associated with the analysis of homogeneous discrete networks of interacting dynamical elements. This book investigates the nonlinear dynamics of peculiar discrete media made up of interconnected phase synchronization systems. After an introduction which sets out the nature of the problem, the book goes on to consider dynamic processes in chain and lattice networks, utilising both continuous and discrete synchronization systems as component elements. Computational studies aimed at oscillatory-wave phenomena will make the book valuable for specialists in radio engineering, biological excitable media and other branches of physics and biology as well as specialists in applied mathematics and nonlinear sciences.
Stability Structures And Chaos In Nonlinear Synchronization Networks
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Author : Valentin Senderovich Afra?movich
language : en
Publisher: World Scientific
Release Date : 1994
Stability Structures And Chaos In Nonlinear Synchronization Networks written by Valentin Senderovich Afra?movich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
The understanding of fields and media using discrete lattice models has been greatly aided by the advent of powerful computers. This has also led to the formulation of new and inspiring problems associated with the analysis of homogeneous discrete networks of interacting dynamical elements. This book investigates the nonlinear dynamics of peculiar discrete media made up of interconnected phase synchronization systems. After an introduction which sets out the nature of the problem, the book goes on to consider dynamic processes in chain and lattice networks, utilising both continuous and discrete synchronization systems as component elements. Computational studies aimed at oscillatory-wave phenomena will make the book valuable for specialists in radio engineering, biological excitable media and other branches of physics and biology as well as specialists in applied mathematics and nonlinear sciences.
Chaos Synchronization And Structures In Dynamics Of Systems With Cylindrical Phase Space
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Author : Nikolai Verichev
language : en
Publisher: Springer Nature
Release Date : 2020-01-01
Chaos Synchronization And Structures In Dynamics Of Systems With Cylindrical Phase Space written by Nikolai Verichev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Science categories.
This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc.
Introduction To Control Of Oscillations And Chaos
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Author : Aleksandr L?vovich Fradkov
language : en
Publisher: World Scientific
Release Date : 1998
Introduction To Control Of Oscillations And Chaos written by Aleksandr L?vovich Fradkov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.
Deterministic Nonlinear Systems
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Author : Vadim S. Anishchenko
language : en
Publisher: Springer
Release Date : 2014-06-16
Deterministic Nonlinear Systems written by Vadim S. Anishchenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-16 with Science categories.
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
14th Chaotic Modeling And Simulation International Conference
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Author : Christos H. Skiadas
language : en
Publisher: Springer Nature
Release Date : 2022-06-13
14th Chaotic Modeling And Simulation International Conference written by Christos H. Skiadas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-13 with Science categories.
Gathering the proceedings of the 14th CHAOS2021 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies. Chapter "On the Origin of the Universe: Chaos or Cosmos" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com
Chaotic Dynamics In Two Dimensional Noninvertible Maps
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Author : Alexandra Barugola
language : en
Publisher: World Scientific
Release Date : 1996-07-29
Chaotic Dynamics In Two Dimensional Noninvertible Maps written by Alexandra Barugola and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-29 with Science categories.
This book is essentially devoted to complex properties (Phase plane structure and bifurcations) of two-dimensional noninvertible maps, i.e. maps having either a non-unique inverse, or no real inverse, according to the plane point. They constitute models of sets of discrete dynamical systems encountered in Engineering (Control, Signal Processing, Electronics), Physics, Economics, Life Sciences. Compared to the studies made in the one-dimensional case, the two-dimensional situation remained a long time in an underdeveloped state. It is only since these last years that the interest for this research has increased. Therefore the book purpose is to give a global presentation of a matter, available till now only in a partial form. Fundamental notions and tools (such as “critical manifolds”), as the most part of results, are accompanied by many examples and figures.
Dynamics Of Nonlinear And Disordered Systems
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Author : Gustavo Mart¡nez-Mekler
language : en
Publisher: World Scientific
Release Date : 1995
Dynamics Of Nonlinear And Disordered Systems written by Gustavo Mart¡nez-Mekler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
This book deals with a series of topics on the cutting edge of nonlinear science, striking a balance between theory and experiment. It consists of two innovative introductory presentations on dynamical systems and fluid dynamics and six chapters on advanced research. A nontrivial interrelation between the different topics becomes apparent throughout the book as an indication of the underlying unity and genericity of nonlinear phenomena. There is a continuous emphasis on conceptual issues often introduced via concrete examples. A common feature is that most of the systems under study are extended, nonhomogeneous and far from equilibrium. The book also exhibits an interesting interplay between deterministic and stochastic approaches.
Analysis Of Complex Nonlinear Mechanical Systems The A Computer Algebra Assisted Approach With Diskette Of Maple Programming
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Author : Martin Lesser
language : en
Publisher: World Scientific Publishing Company
Release Date : 1995-09-20
Analysis Of Complex Nonlinear Mechanical Systems The A Computer Algebra Assisted Approach With Diskette Of Maple Programming written by Martin Lesser and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-20 with Science categories.
The book covers the fundamentals of the mechanics of multibody systems, i.e., systems of interconnected rigid bodies. A geometric view is emphasized in which the techniques and algorithms are motivated by the picture of the rigid body system as a point in the multidimensional space of all possible configurations. The reader is introduced to computer algebra methods in the form of a system, called Sophia, which is implemented in the Maple symbolic manipulation system. The first chapter provides a motivational introduction to the basic principles and an introduction to Maple. Kinematics based on the idea of tangent vectors to the configuration manifold sets the stage for dynamical analysis. The latter ranges from the Lagrange and Gibbs-Appell to Kane's equations. Coverage includes nonholonomic systems and redundant variable methods. The computer algebra methods included enable the treatment of nontrivial mechanical systems and the development of efficient numerical codes for simulation.
Introduction To Nonlinear Oscillations
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Author : Vladimir I. Nekorkin
language : en
Publisher: John Wiley & Sons
Release Date : 2016-05-02
Introduction To Nonlinear Oscillations written by Vladimir I. Nekorkin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-02 with Science categories.
A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.