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Chaos, synchronization and structure...

Erofeev, Vladimir.

Chaos, synchronization and structures in dynamics of systems with cylindrical phase space

Record Type:	Electronic resources : Monograph/item
Title/Author:	Chaos, synchronization and structures in dynamics of systems with cylindrical phase spaceby Nikolai Verichev, Stanislav Verichev, Vladimir Erofeev.
Author:	Verichev, Nikolai.
other author:	Verichev, Stanislav.
Published:	Cham :Springer International Publishing :2020.
Description:	xii, 197 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Rotational motion.
Online resource:	https://doi.org/10.1007/978-3-030-36103-7
ISBN:	9783030361037$q(electronic bk.)

Chaos, synchronization and structures in dynamics of systems with cylindrical phase space
Verichev, Nikolai.

Chaos, synchronization and structures in dynamics of systems with cylindrical phase space[electronic resource] /by Nikolai Verichev, Stanislav Verichev, Vladimir Erofeev. - Cham :Springer International Publishing :2020. - xii, 197 p. :ill. (some col.), digital ;24 cm. - Understanding complex systems,1860-0832. - Understanding complex systems..

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.

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.

ISBN: 9783030361037$q(electronic bk.)

Standard No.: 10.1007/978-3-030-36103-7doiSubjects--Topical Terms:

251518
Rotational motion.

LC Class. No.: QC133 / .V475 2020

Dewey Class. No.: 531.34

Chaos, synchronization and structures in dynamics of systems with cylindrical phase space
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245 1 0 $a Chaos, synchronization and structures in dynamics of systems with cylindrical phase space $h [electronic resource] / $c by Nikolai Verichev, Stanislav Verichev, Vladimir Erofeev.
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300 $a xii, 197 p. : $b ill. (some col.), digital ; $c 24 cm.
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505 0 $a 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.
520 $a 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.
650 0 $a Rotational motion. $3 251518
650 0 $a Chaotic behavior in systems. $3 182904
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650 2 4 $a Applications of Nonlinear Dynamics and Chaos Theory. $3 760027
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700 1 $a Verichev, Stanislav. $3 863996
700 1 $a Erofeev, Vladimir. $3 511953
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