November 26, 2020

Download Ebook Free Poincaré-Andronov-Melnikov Analysis For Non-Smooth Systems

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems
Author : Michal Fečkan,Michal Pospíšil
Publisher : Academic Press
Release Date : 2016-06-07
Category : Mathematics
Total pages :260
GET BOOK

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity. Extends Melnikov analysis of the classic Poincaré and Andronov staples, pointing to a general theory for freedom in dimensions of spatial variables and parameters as well as asymptotical results such as stability, instability, and hyperbolicity Presents a toolbox of critical theoretical techniques for many practical examples and models, including non-smooth dynamical systems Provides realistic models based on unsolved discontinuous problems from the literature and describes how Poincaré-Andronov-Melnikov analysis can be used to solve them Investigates the relationship between non-smooth systems and their continuous approximations

Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts

Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts
Author : Olejnik Pawel,Feckan Michal,Awrejcewicz Jan
Publisher : #N/A
Release Date : 2017-07-07
Category : Mathematics
Total pages :276
GET BOOK

This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics.

Mathematical Modelling in Health, Social and Applied Sciences

Mathematical Modelling in Health, Social and Applied Sciences
Author : Hemen Dutta
Publisher : Springer Nature
Release Date : 2020-02-29
Category : Mathematics
Total pages :320
GET BOOK

This book discusses significant research findings in the field of mathematical modelling, with particular emphasis on important applied-sciences, health, and social issues. It includes topics such as model on viral immunology, stochastic models for the dynamics of influenza, model describing the transmission of dengue, model for human papillomavirus (HPV) infection, prostate cancer model, realization of economic growth by goal programming, modelling of grazing periodic solutions in discontinuous systems, modelling of predation system, fractional epidemiological model for computer viruses, and nonlinear ecological models. A unique addition in the proposed areas of research and education, this book is a valuable resource for graduate students, researchers and educators associated with the study of mathematical modelling of health, social and applied-sciences issues. Readers interested in applied mathematics should also find this book valuable.

Elements of Applied Bifurcation Theory

Elements of Applied Bifurcation Theory
Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Release Date : 2013-03-09
Category : Mathematics
Total pages :632
GET BOOK

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Mathematical Reviews

Mathematical Reviews
Author : Anonim
Publisher : Unknown
Release Date : 2000
Category : Mathematics
Total pages :129
GET BOOK

Non-Smooth Dynamical Systems

Non-Smooth Dynamical Systems
Author : Markus Kunze
Publisher : Springer
Release Date : 2007-05-06
Category : Mathematics
Total pages :232
GET BOOK

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.

Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems
Author : Gerald Teschl
Publisher : American Mathematical Soc.
Release Date : 2012-08-30
Category : Mathematics
Total pages :356
GET BOOK

This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Elements of Applied Bifurcation Theory

Elements of Applied Bifurcation Theory
Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Release Date : 1998-09-18
Category : Mathematics
Total pages :594
GET BOOK

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Distribution of Sequences

Distribution of Sequences
Author : Oto Strauch,Štefan Porubský
Publisher : Peter Lang Publishing
Release Date : 2005
Category : Distribution (Probability theory)
Total pages :570
GET BOOK

The monograph covers material scattered throughout books and journals and focuses on the distribution properties of sequences which may be expressed in terms of distribution function, upper and lower distribution function, the discrepancy, diaphony, dispersion etc. The individual character of sequences reflected in their distribution properties may be an object of study from various points of view, and as such they are often the primary goal of investigation. In that case the studied properties are caught in separate results and are consequently accessible in a displayed form. On the other hand, the various distribution properties of sequences play only a subsidiary role in proofs and thus remain often hidden and are not manifested in a visible form. The enormous wealth of information contained in both cases may be of value not only to those working directly in the field, but also to those working in related branches of number theory, combinatorics, real or numerical analysis in the process of finding sequence possessing the required properties. Last, but not least browsing throughout the book may provide the impetus for prospective further research. This is what we hope may address a wide class of working mathematicians.

Introduction to Applied Nonlinear Dynamical Systems and Chaos

Introduction to Applied Nonlinear Dynamical Systems and Chaos
Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Release Date : 2006-04-18
Category : Mathematics
Total pages :844
GET BOOK

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik

Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications
Author : Carmen Chicone
Publisher : Springer Science & Business Media
Release Date : 2008-04-08
Category : Mathematics
Total pages :563
GET BOOK

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.

Introduction to Mechanics and Symmetry

Introduction to Mechanics and Symmetry
Author : Jerrold E. Marsden,Tudor S. Ratiu
Publisher : Springer Science & Business Media
Release Date : 2013-03-19
Category : Science
Total pages :586
GET BOOK

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.

Normal Modes and Localization in Nonlinear Systems

Normal Modes and Localization in Nonlinear Systems
Author : Alexander F. Vakakis,Leonid I. Manevitch,Yuri V. Mikhlin,Valery N. Pilipchuk,Alexandr A. Zevin
Publisher : John Wiley & Sons
Release Date : 2008-07-11
Category : Science
Total pages :552
GET BOOK

This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.

Bifurcation and Chaos in Nonsmooth Mechanical Systems

Bifurcation and Chaos in Nonsmooth Mechanical Systems
Author : Jan Awrejcewicz,Claude-Henri Lamarque
Publisher : World Scientific
Release Date : 2003
Category : Science
Total pages :543
GET BOOK

This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.

Nonlinear Oscillations and Waves in Dynamical Systems

Nonlinear Oscillations and Waves in Dynamical Systems
Author : P.S Landa
Publisher : Springer Science & Business Media
Release Date : 2013-06-29
Category : Mathematics
Total pages :544
GET BOOK

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.