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Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space
Buch von Nikolai Verichev (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details
Erscheinungsjahr: 2020
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 212
Reihe: Understanding Complex Systems
Inhalt: xii
197 S.
97 s/w Illustr.
28 farbige Illustr.
197 p. 125 illus.
28 illus. in color.
ISBN-13: 9783030361020
ISBN-10: 3030361020
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Verichev, Nikolai
Erofeev, Vladimir
Verichev, Stanislav
Auflage: 1st ed. 2020
Hersteller: Springer International Publishing
Understanding Complex Systems
Maße: 241 x 160 x 18 mm
Von/Mit: Nikolai Verichev (u. a.)
Erscheinungsdatum: 02.01.2020
Gewicht: 0,489 kg
preigu-id: 117596283
Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details
Erscheinungsjahr: 2020
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 212
Reihe: Understanding Complex Systems
Inhalt: xii
197 S.
97 s/w Illustr.
28 farbige Illustr.
197 p. 125 illus.
28 illus. in color.
ISBN-13: 9783030361020
ISBN-10: 3030361020
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Verichev, Nikolai
Erofeev, Vladimir
Verichev, Stanislav
Auflage: 1st ed. 2020
Hersteller: Springer International Publishing
Understanding Complex Systems
Maße: 241 x 160 x 18 mm
Von/Mit: Nikolai Verichev (u. a.)
Erscheinungsdatum: 02.01.2020
Gewicht: 0,489 kg
preigu-id: 117596283
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