Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space

by Nikolai Verichev, Stanislav Verichev, Vladimir Erofeev

Overview

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.

Product Details

ISBN-13:	9783030361020
Publisher:	Springer International Publishing
Publication date:	01/02/2020
Series:	Understanding Complex Systems
Edition description:	1st ed. 2020
Pages:	197
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of 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.