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Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space / by Nikolai Verichev, Stanislav Verichev, Vladimir Erofeev.
- Format:
- Book
- Author/Creator:
- Verichev, Nikolai, author.
- Verichev, Stanislav, author.
- Erofeev, Vladimir, author.
- Series:
- Physics and Astronomy (Springer-11651)
- Understanding complex systems 1860-0832
- Understanding Complex Systems, 1860-0832
- Language:
- English
- Subjects (All):
- Statistical physics.
- Computational complexity.
- Physics.
- Mathematical physics.
- Statistical Physics and Dynamical Systems.
- Complexity.
- Applications of Nonlinear Dynamics and Chaos Theory.
- Mathematical Methods in Physics.
- Mathematical Physics.
- Local Subjects:
- Statistical Physics and Dynamical Systems.
- Complexity.
- Applications of Nonlinear Dynamics and Chaos Theory.
- Mathematical Methods in Physics.
- Mathematical Physics.
- Physical Description:
- 1 online resource (XII, 197 pages) : 125 illustrations, 28 illustrations in color.
- Edition:
- First edition 2020.
- Contained In:
- Springer eBooks
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2020.
- System Details:
- text file PDF
- Summary:
- 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, id est 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, et cetera .
- Contents:
- Introduction
- Autonomous and non-autonomous systems with one degrees-of-freedom. Autonomous and non-autonomous systems with one and a half degrees-of-freedom
- Autonomous systems with two degrees-of-freedom
- Vibration of shafts
- Synchronization in homogeneous lattices
- Physics, existence, fusion and stability Of cluster structures
- Appendix I
- Appendix II.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-030-36103-7
- 9783030361037
- Access Restriction:
- Restricted for use by site license.
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