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Two-Dimensional Quadratic Nonlinear Systems Volume I: Univariate Vector Fields

Posted By: AvaxGenius
Two-Dimensional Quadratic Nonlinear Systems Volume I: Univariate Vector Fields

Two-Dimensional Quadratic Nonlinear Systems Volume I: Univariate Vector Fields by Albert C. J. Luo
English | PDF,EPUB | 2023 | 692 Pages | ISBN : 9811678723 | 106.6 MB

This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering.

Hard Ball Systems and the Lorentz Gas

Posted By: Jeembo
Hard Ball Systems and the Lorentz Gas

Hard Ball Systems and the Lorentz Gas by L.A. Bunimovich, D. Burago, N. Chernov
English | 2000 | ISBN: 3642087116 | 458 Pages | PDF | 10.0 MB

Hard Ball Systems and the Lorentz Gas are fundamental models arising in the theory of Hamiltonian dynamical systems.

"Dynamical Systems: Qualitative and Computational Aspects" ed. by Kamal Shah, Bruno Carpentieri, Arshad Ali

Posted By: exLib
"Dynamical Systems: Qualitative and Computational Aspects" ed. by Kamal Shah, Bruno Carpentieri, Arshad Ali

"Dynamical Systems: Qualitative and Computational Aspects" ed. by Kamal Shah, Bruno Carpentieri, Arshad Ali
ITexLi | 2023 | ISBN: 1803565675 9781803565675 1803565667 9781803565668 1803565683 9781803565682 | 153 pages | PDF | 8 MB

This book provides an overview of the current state of the art in this fascinating and critically important field of pure and applied mathematics, presenting recent developments in theory, modeling, algorithms, and applications.

Integrable Systems in the Realm of Algebraic Geometry (Repost)

Posted By: AvaxGenius
Integrable Systems in the Realm of Algebraic Geometry (Repost)

Integrable Systems in the Realm of Algebraic Geometry by Pol Vanhaecke
English | PDF | 2001 | 78 Pages | ISBN : 3540423370 | 95.3 MB

This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way. Special attention is drawn to algebraic completely integrable systems. Several integrable systems are constructed and studied in detail and a few applications of integrable systems to algebraic geometry are worked out. In the second edition some of the concepts in Poisson geometry are clarified by introducting Poisson cohomology; the Mumford systems are constructed from the algebra of pseudo-differential operators, which clarifies their origin; a new explanation of the multi Hamiltonian structure of the Mumford systems is given by using the loop algebra of sl(2); and finally Goedesic flow on SO(4) is added to illustrate the linearizatin algorith and to give another application of integrable systems to algebraic geometry.

Dynamical Systems with Applications using MATLAB®

Posted By: AvaxGenius
Dynamical Systems with Applications using MATLAB®

Dynamical Systems with Applications using MATLAB® by Stephen Lynch
English | PDF(True) | 2004 | 458 Pages | ISBN : 0817643214 | 26.9 MB

Beginning with a tutorial guide to MATLAB®, the text thereafter is divided into two main areas. In Part I, both real and complex discrete dynamical systems are considered, with examples presented from population dynamics, nonlinear optics, and materials science. Part II includes examples from mechanical systems, chemical kinetics, electric circuits, economics, population dynamics, epidemiology, and neural networks. Common themes such as bifurcation, bistability, chaos, fractals, instability, multistability, periodicity, and quasiperiodicity run through several chapters. Chaos control and multifractal theories are also included along with an example of chaos synchronization. Some material deals with cutting-edge published research articles and provides a useful resource for open problems in nonlinear dynamical systems.

Nonlinear Dynamical Control Systems

Posted By: AvaxGenius
Nonlinear Dynamical Control Systems

Nonlinear Dynamical Control Systems by Henk Nijmeijer, Arjan Schaft
English | PDF | 1990 | 480 Pages | ISBN : 038797234X | 26.3 MB

This book has recently been retypeset in LaTeX for clearer presentation.
This textbook on the differential geometric approach to nonlinear control grew out of a set of lecture notes, which were prepared for a course on nonlinear system theory, given by us for the first time during the fall semester of 1988. The audience consisted mostly of graduate students , taking part in the Dutch national Graduate Program on Systems and Control.

Modal Analysis of Nonlinear Mechanical Systems (Repost)

Posted By: AvaxGenius
Modal Analysis of Nonlinear Mechanical Systems (Repost)

Modal Analysis of Nonlinear Mechanical Systems by Gaetan Kerschen
English | PDF | 2014 | 346 Pages | ISBN : 3709117909 | 6.8 MB

The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.

Wavelets in Neuroscience (Repost)

Posted By: AvaxGenius
Wavelets in Neuroscience (Repost)

Wavelets in Neuroscience by Alexander E. Hramov, Alexey A. Koronovskii, Valeri A. Makarov, Alexey N. Pavlov, Evgenia Sitnikova
English | PDF(True) | 2015 | 331 Pages | ISBN : 3662438496 | 13.24 MB

This book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade.

Mathematical and Computational Modeling and Simulation: Fundamentals and Case Studies

Posted By: AvaxGenius
Mathematical and Computational Modeling and Simulation: Fundamentals and Case Studies

Mathematical and Computational Modeling and Simulation: Fundamentals and Case Studies by Dietmar P. F. Moeller
English | PDF | 2004 | 438 Pages | ISBN : 3540403892 | 29.2 MB

Mathematical and Computational Modeling and Simulation - a highly multi-disciplinary field with ubiquitous applications in science and engineering - is one of the key enabling technologies of the 21st century. This book introduces to the use of Mathematical and Computational Modeling and Simulation in order to develop an understanding of the solution characteristics of a broad class of real-world problems. The relevant basic and advanced methodologies are explained in detail, with special emphasis on ill-defined problems. Some 15 simulation systems are presented on the language and the logical level. Moreover, the reader can accumulate experience by studying a wide variety of case studies. The latter are briefly described within the book but their full versions as well as some simulation software demos are available on the Web. The book can be used for University courses of different level as well as for self-study. Advanced sections are marked and can be skipped in a first reading or in undergraduate courses.

Springer-Handbuch der Mathematik IV

Posted By: AvaxGenius
Springer-Handbuch der Mathematik IV

Springer-Handbuch der Mathematik IV: Begründet von I.N. Bronstein und K.A. Semendjaew Weitergeführt von G. Grosche, V. Ziegler und D. Ziegler Herausgegeben von E. Zeidler by Eberhard Zeidler
Deutsch | PDF(True) | 2013 | 634 Pages | ISBN : 3658002883 | 6.2 MB

Als mehrbändiges Nachschlagewerk ist das Springer-Handbuch der Mathematik in erster Linie für wissenschaftliche Bibliotheken, akademische Institutionen und Firmen sowie interessierte Individualkunden in Forschung und Lehre gedacht. Es ergänzt das einbändige themenumfassende Springer-Taschenbuch der Mathematik (ehemaliger Titel Teubner-Taschenbuch der Mathematik), das sich in seiner begrenzten Stoffauswahl besonders an Studierende richtet. Teil IV des Springer-Handbuchs enthält die folgenden Zusatzkapitel zum Springer-Taschenbuch: Höhere Analysis, Lineare sowie Nichtlineare Funktionalanalysis und ihre Anwendungen, Dynamische Systeme, Nichtlineare partielle Differentialgleichungen, Mannigfaltigkeiten, Riemannsche Geometrie und allgemeine Relativitätstheorie, Liegruppen, Liealgebren und Elementarteilchen, Topologie, Krümmung und Analysis.

Probability, Random Processes, and Ergodic Properties

Posted By: AvaxGenius
Probability, Random Processes, and Ergodic Properties

Probability, Random Processes, and Ergodic Properties by Robert M. Gray
English | PDF(True) | 2009 | 348 Pages | ISBN : 1441910891 | 3.23 MB

Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing. It will also interest those working with random or stochastic processes, including mathematicians, statisticians, and economists.

Dynamical Systems V: Bifurcation Theory and Catastrophe Theory

Posted By: AvaxGenius
Dynamical Systems V: Bifurcation Theory and Catastrophe Theory

Dynamical Systems V: Bifurcation Theory and Catastrophe Theory by V. I. Arnol’d
English | PDF | 1994 | 279 Pages | ISBN : 3540181733 | 19.1 MB

Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems.

Die Erforschung des Chaos: Eine Einführung für Naturwissenschaftler und Ingenieure

Posted By: AvaxGenius
Die Erforschung des Chaos: Eine Einführung für Naturwissenschaftler und Ingenieure

Die Erforschung des Chaos: Eine Einführung für Naturwissenschaftler und Ingenieure by John Argyris, Gunter Faust, Maria Haase
Deutsch | PDF | 1994 | 811 Pages | ISBN : 3322904423 | 20.7 MB

Das Buch stellt die grundlegenden Konzepte der Chaos-Theorie und die mathematischen Hilfsmittel so elementar wie möglich dar.
Es war unser Wunsch, mit diesem Band ein einführendes Lehrbuch in die Theorie des Chaos zu präsentieren. Wir wenden uns an Physiker und Ingenieure, die sich im Rahmen von nicht linearen deterministischen Systemen mit dieser neuen, aufregenden Wissenschaft vertraut machen wollen. Bei einem solchen Lehrbuch ist die Mathematik selbstverständlich ein unerläßliches Werkzeug; wir haben es deshalb nicht unterlassen, auch komplexe mathematische Probleme anzusprechen, auch wenn wir es - aufgrund unseres Werdegangs und unserer philosophischen Einstellung - im allgemeinen vorziehen, die Aufmerksamkeit des Lesers auf ein physikalisches Verständnis der Phänomene zu lenken.

The Three-body Problem from Pythagoras to Hawking

Posted By: AvaxGenius
The Three-body Problem from Pythagoras to Hawking

The Three-body Problem from Pythagoras to Hawking by Mauri Valtonen, Joanna Anosova, Konstantin Kholshevnikov, Aleksandr Mylläri, Victor Orlov, Kiyotaka Tanikawa
English | True PDF | 2016 | 183 Pages | ISBN : 3319227254 | 5.2 MB

This book, written for a general readership, reviews and explains the three-body problem in historical context reaching to latest developments in computational physics and gravitation theory. The three-body problem is one of the oldest problems in science and it is most relevant even in today’s physics and astronomy.

Exterior Differential Systems and the Calculus of Variations

Posted By: AvaxGenius
Exterior Differential Systems and the Calculus of Variations

Exterior Differential Systems and the Calculus of Variations by Phillip A. Griffiths
English | PDF | 1983 | 348 Pages | ISBN : 0817631038 | 14.6 MB

This monograph is a revised and expanded version of lecture notes from a class given at Harvard University, Nankai University, and the Graduate School of the Academia Sinica during the academic year 1981-82. The objective was to present the formalism, together with numerous illustrative examples, of the calculus of variations for functionals whose domain of definition consists of integral manifolds of an exterior differential system. This includes as a special case the Lagrange problem of analyzing classical functionals with arbitrary (i.e., nonholonomic as well as holonomic) constraints. A secondary objective was to illustrate in practice some aspects of the theory of exterior differential systems. In fact, even though the calculus of variations is a venerable subject about which it is hard to say something new, (l) we feel that utilizing techniques from exterior differential systems such as Cauchy characteristics, the derived flag, and prolongation allows a systematic treatment of the subject in greater generality than customary and sheds new light on even the classical Lagrange problem.