Showing results for "Normal Modes and Localization in Nonlinear Systems English"

Exact analytical solutions to periodic motions in nonlinear dynamical systems are almost not possible. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. However, the perturbation methods cannot provide the enough accuracy of analytical solutions of periodic motions in nonlinear dynamical systems. So the bifurcation trees of periodic motions to chaos cannot be achieved...

This book brings together 12 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigate...

This book focuses on the development of three novel approaches to build up a framework for the frequency domain analysis and design of nonlinear systems. The concepts are derived from Volterra series representation of nonlinear systems which are described by nonlinear difference or differential equations. Occupying the middle ground between traditional linear approaches and more complex nonlinear system theories, the book will help readers to have a good start to analyse and exploit the no...

This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular promine...

This book provides scalable, effective and real-world-compatible methods and algorithms for the control and extended estimation of uncertain nonlinear systems against a backdrop of often-unconventional problems. The author provides advice on choosing which solution is most relevant to the desired control objectives, the nature of present uncertainties and the impact on closed-loop performance.The book introduces its key paradigms step by step and then presents the family of candida...

This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, cont...

This book highlights the presentation of methods for studying oscillations under external periodic influence and random changes in parameters in dynamic systems with nonlinearities that have discontinuities and kinks. The analysis of dynamic systems is based on effective approaches and algorithms of the method of point mappings of Poincaré surfaces, developed by the Nizhny Novgorod Scientific School of academician A.A. Andronov. Considerable attention is paid to the study of the general pi...

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discu...

This book provides rich and varied insights into a diverse range of writing systems, including Chinese, Japanese, Korean, Alphasyllabaries (Abugidas), Abjads, and other lesser-studied writing systems. It also covers alphabetic writing systems with diacritics, such as Roman script. These writing systems contrast with the Roman script used for English, which is written in a left-to-right linear order without diacritics. This book explores the challenges of learning to read and write these di...

The book Control of Nonlinear Systems–Stability and Performance fills a crucial gap in the field of nonlinear control systems by providing a comprehensive yet accessible treatment of the subject. Unlike many existing texts that are either too complex for beginners or omit essential topics, this book strikes the right balance of mathematical rigor and practicality.The main objective of the book is to simplify and unify the existing techniques for designing ...

This book is a compilation of select chapter from the 2023 International Conference on Nonlinear Science and Complexity. It presents recent advancements, discoveries, and ongoing research in various facets of nonlinear science and complexity. The book covers a broad scope of topics, including nonlinear dynamical systems, complex systems, quantum sensing, and mathematical approaches in biological and economic models. Key subspecialties addressed include nonlinear differential equations, mod...

This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments.While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter i...