Overview
- Summarizes the results of analytical studies on dynamical chaos, synchronization, and dynamic structures in systems of coupled rotators
- Focuses on the dynamics of systems with a cylindrical phase space, also referred to as rotators
- Covers autonomous and nonautonomous systems with one, one-and-a-half, and two or more degrees of freedom
- Presents a classification system for dynamic structures that can arise in systems with a large number of interconnected objects
Part of the book series: Understanding Complex Systems (UCS)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 systemswith 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.
Authors and Affiliations
About the authors
Dr. N.N. Verichev specializes in the field of the qualitative theory of dynamical systems, oscillation theory, nonlinear dynamics, dynamic chaos, and chaotic synchronization. He has discovered the effect of chaotic synchronization of nonidentical systems (1985).
Dr.S.N. Verichev graduated from Nizhny Novgorod State University in 1998 (M.Sc. in Physics), got his Ph.D. degree in TU Delft (2002), and has 18 years of international R&D experience in nonlinear dynamics as well as such practical fields as dredging and mining, oil & gas, civil and mechanical engineering, and deep-sea mining.
Prof. V.I. Erofeev got his Ph.D./Dr. Habil. degrees in Nizhny Novgorod State University (1986, 1994). He has proposed new methods of nondestructive testing of materials and structures, developed scientific foundations of vibration protection systems for machines and structures using inertia and dissipation of rheological media, and performed a series of studies on the chaotic dynamics of mechanical systems with energy sources of limited power, as well as on the existence and stability of stationary cluster structures in homogeneous chains of dissipative coupled rotators.
Bibliographic Information
Book Title: Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space
Authors: Nikolai Verichev, Stanislav Verichev, Vladimir Erofeev
Series Title: Understanding Complex Systems
DOI: https://doi.org/10.1007/978-3-030-36103-7
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-36102-0Published: 02 January 2020
Softcover ISBN: 978-3-030-36105-1Published: 02 January 2021
eBook ISBN: 978-3-030-36103-7Published: 01 January 2020
Series ISSN: 1860-0832
Series E-ISSN: 1860-0840
Edition Number: 1
Number of Pages: XII, 197
Number of Illustrations: 97 b/w illustrations, 28 illustrations in colour
Topics: Statistical Physics and Dynamical Systems, Complexity, Applications of Nonlinear Dynamics and Chaos Theory, Mathematical Methods in Physics, Mathematical Physics