Alexander Balanov's Books

Synchronization

From Simple to Complex

By: Alexander Balanov,Natalia Janson,Dmitry Postnov,Olga Sosnovtseva

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Synchronization

From Simple to Complex

By: Alexander Balanov,Natalia Janson,Dmitry Postnov,Olga Sosnovtseva

This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.

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426

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540721282

ISBN 13

9783540721284

Nonlinear Dynamics of Chaotic and Stochastic Systems

Tutorial and Modern Developments

By: Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier

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Nonlinear Dynamics of Chaotic and Stochastic Systems

Tutorial and Modern Developments

By: Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier

We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

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Page Count

463

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540381686

ISBN 13

9783540381686

Geometric Methods in Degree Theory for Equivariant Maps

By: Alexander M. Kushkuley,Zalman I. Balanov

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Geometric Methods in Degree Theory for Equivariant Maps

By: Alexander M. Kushkuley,Zalman I. Balanov

The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces. A list of the problems discussed includes Borsuk-Ulam type theorems for degrees of equivariant maps in finite and infinite dimensional cases, extensions of equivariant maps and equivariant homotopy classification, genus and G-category, elliptic boundary value problem, equivalence of p-group representations. The new results and geometric clarification of several known theorems presented here will make it interesting and useful for specialists in equivariant topology and its applications to non-linear analysis and representation theory.

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143

Publisher

Springer

Published Date

ISBN 10

3540687262

ISBN 13

9783540687269

Multistability in Physical and Living Systems

Characterization and Applications

By: Alexander N. Pisarchik,Alexander E. Hramov

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Multistability in Physical and Living Systems

Characterization and Applications

By: Alexander N. Pisarchik,Alexander E. Hramov

This book starts with an introduction to the basic concepts of multistability, then illustrates how multistability arises in different systems and explains the main mechanisms of multistability emergence. A special attention is given to noise which can convert a multistable deterministic system to a monostable stochastic one. Furthermore, the most important applications of multistability in different areas of science, engineering and technology are given attention throughout the book, including electronic circuits, lasers, secure communication, and human perception. The book aims to provide a first approach to multistability for readers, who are interested in understanding its fundamental concepts and applications in several fields. This book will be useful not only to researchers and engineers focusing on interdisciplinary studies, but also to graduate students and technicians. Both theoreticians and experimentalists will rely on it, in fields ranging from mathematics and laser physics to neuroscience and astronomy. The book is intended to fill a gap in the literature, to stimulate new discussions and bring some fundamental issues to a deeper level of understanding of the mechanisms underlying self-organization of matter and world complexity.

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Page Count

417

Publisher

Springer Nature

Published Date

ISBN 10

303098396X

ISBN 13

9783030983963

Wavelets in Neuroscience

By: Alexander E. Hramov,Alexey A. Koronovskii,Valeri A. Makarov,Vladimir A. Maksimenko,Alexey N. Pavlov,Evgenia Sitnikova

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Wavelets in Neuroscience

By: Alexander E. Hramov,Alexey A. Koronovskii,Valeri A. Makarov,Vladimir A. Maksimenko,Alexey N. Pavlov,Evgenia Sitnikova

This book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks. It also demonstrates how and where wavelet-based mathematical tools can provide an advantage over classical approaches used in neuroscience. The authors well describe single neuron and populational neural recordings. This 2nd edition discusses novel areas and significant advances resulting from experimental techniques and computational approaches developed since 2015, and includes three new topics: • Detection of fEPSPs in multielectrode LFPs recordings. • Analysis of Visual Sensory Processing in the Brain and BCI for Human Attention Control; • Analysis and Real-time Classification of Motor-related EEG Patterns; The book is a valuable resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related areas.

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Page Count

384

Publisher

Springer Nature

Published Date

ISBN 10

303075992X

ISBN 13

9783030759926

Synchronization

From Coupled Systems to Complex Networks

By: Stefano Boccaletti,Alexander N. Pisarchik,Charo I. del Genio,Andreas Amann

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Synchronization

From Coupled Systems to Complex Networks

By: Stefano Boccaletti,Alexander N. Pisarchik,Charo I. del Genio,Andreas Amann

A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will help advanced graduate students and researchers gain an organic and complete understanding of the subject.

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Page Count

268

Publisher

Cambridge University Press

Published Date

ISBN 10

1108640036

ISBN 13

9781108640039

Emergence Of Dynamical Order: Synchronization Phenomena In Complex Systems

By: Susanna C Manrubia,Alexander S Mikhailov,Damian H Zanette

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Emergence Of Dynamical Order: Synchronization Phenomena In Complex Systems

By: Susanna C Manrubia,Alexander S Mikhailov,Damian H Zanette

Synchronization processes bring about dynamical order and lead to spontaneous development of structural organization in complex systems of various origins, from chemical oscillators and biological cells to human societies and the brain. This book provides a review and a detailed theoretical analysis of synchronization phenomena in complex systems with different architectures, composed of elements with periodic or chaotic individual dynamics. Special attention is paid to statistical concepts, such as nonequilibrium phase transitions, order parameters and dynamical glasses.

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Page Count

359

Publisher

World Scientific

Published Date

ISBN 10

9814482951

ISBN 13

9789814482950

Quantum Mechanics

By: Mark Julian Everitt,Kieran Niels Bjergstrom,Stephen Neil Alexander Duffus

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Quantum Mechanics

By: Mark Julian Everitt,Kieran Niels Bjergstrom,Stephen Neil Alexander Duffus

QUANTUM MECHANICS From classical analytical mechanics to quantum mechanics, simulation, foundations & engineering Quantum mechanics is a fundamental and conceptually challenging area of physics. It is usually assumed that students are unfamiliar with Lagrangian and Hamiltonian formulations of classical mechanics and the role played by probability. As a result, quantum physics is typically introduced using heuristic arguments, obscuring synergies with classical mechanics. This book takes an alternative approach by leveraging classical analytical mechanics to facilitate a natural transition to quantum physics. By doing so, a solid foundation for understanding quantum phenomena is provided. Key features of this textbook include: Mathematics and Classical Analytical Mechanics: The necessary mathematical background and classical analytical mechanics are introduced gradually, allowing readers to focus on one conceptual challenge at a time. Deductive Approach: Quantum mechanics is presented on the firm foundation of classical analytical mechanics, ensuring a logical progression of concepts. Pedagogical Features: This book includes helpful notes, worked examples, problems, computational challenges, and problem-solving approaches to enhance understanding. Comprehensive Coverage: Including advanced topics such as open quantum systems, phase-space methods, and computational methods for quantum physics including good programming practice and code design. Much of the code needed to reproduce figures throughout this book is included. Consideration of Foundations: The measurement problem and correspondence principle are addressed, including an open and critical discussion of their interpretation and consequences. Introduction to Quantum Systems Engineering: This is the first book to introduce Quantum Systems Engineering approaches for applied quantum technologies development. This textbook is suitable for undergraduate students in physics and graduate students in mathematics, chemistry, engineering, and materials science.

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Page Count

438

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119829895

ISBN 13

9781119829898

Real Enriques Surfaces

By: Alexander Degtyarev,Ilia Itenberg,Viatcheslav Kharlamov

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Real Enriques Surfaces

By: Alexander Degtyarev,Ilia Itenberg,Viatcheslav Kharlamov

Deformation classes. p. 89.

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284

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540410880

ISBN 13

9783540410881

Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

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Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.

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Page Count

178

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540642072

ISBN 13

9783540642077

Synchronization

From Simple to Complex

By: Alexander Balanov,Natalia Janson,Dmitry Postnov,Olga Sosnovtseva

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Synchronization

From Simple to Complex

By: Alexander Balanov,Natalia Janson,Dmitry Postnov,Olga Sosnovtseva

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Page Count

426

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540721282

ISBN 13

9783540721284

Geometric Methods in Degree Theory for Equivariant Maps

By: Alexander M. Kushkuley,Zalman I. Balanov

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Geometric Methods in Degree Theory for Equivariant Maps

By: Alexander M. Kushkuley,Zalman I. Balanov

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Page Count

143

Publisher

Springer

Published Date

ISBN 10

3540687262

ISBN 13

9783540687269

Book's by Alexander Balanov

Synchronization

Synchronization

Nonlinear Dynamics of Chaotic and Stochastic Systems

Nonlinear Dynamics of Chaotic and Stochastic Systems

Geometric Methods in Degree Theory for Equivariant Maps

Geometric Methods in Degree Theory for Equivariant Maps

Multistability in Physical and Living Systems

Multistability in Physical and Living Systems

Wavelets in Neuroscience

Wavelets in Neuroscience

Synchronization

Synchronization

Emergence Of Dynamical Order: Synchronization Phenomena In Complex Systems

Emergence Of Dynamical Order: Synchronization Phenomena In Complex Systems

Quantum Mechanics

Quantum Mechanics

Real Enriques Surfaces

Real Enriques Surfaces

Integral Geometry, Radon Transforms and Complex Analysis

Integral Geometry, Radon Transforms and Complex Analysis

Synchronization

Synchronization

Geometric Methods in Degree Theory for Equivariant Maps

Geometric Methods in Degree Theory for Equivariant Maps

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