Poincar Andronov Melnikov Analysis for Non Smooth Systems

Poincar   Andronov Melnikov Analysis for Non Smooth Systems
Author: Michal Fečkan,Michal Pospíšil
Publsiher: Academic Press
Total Pages: 260
Release: 2016-06-07
ISBN 10: 0128043644
ISBN 13: 9780128043646
Language: EN, FR, DE, ES & NL

Poincar Andronov Melnikov Analysis for Non Smooth Systems Book Review:

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
Publsiher: #N/A
Total Pages: 276
Release: 2017-07-07
ISBN 10: 9813225300
ISBN 13: 9789813225305
Language: EN, FR, DE, ES & NL

Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts Book Review:

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
Publsiher: Springer Nature
Total Pages: 320
Release: 2020-02-29
ISBN 10: 9811522863
ISBN 13: 9789811522864
Language: EN, FR, DE, ES & NL

Mathematical Modelling in Health Social and Applied Sciences Book Review:

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
Publsiher: Springer Science & Business Media
Total Pages: 632
Release: 2013-03-09
ISBN 10: 1475739788
ISBN 13: 9781475739787
Language: EN, FR, DE, ES & NL

Elements of Applied Bifurcation Theory Book Review:

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
Publsiher: Unknown
Total Pages: 135
Release: 2000
ISBN 10: 1928374650XXX
ISBN 13: UVA:X006089013
Language: EN, FR, DE, ES & NL

Mathematical Reviews Book Review:

Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems
Author: Gerald Teschl
Publsiher: American Mathematical Soc.
Total Pages: 356
Release: 2012-08-30
ISBN 10: 0821883283
ISBN 13: 9780821883280
Language: EN, FR, DE, ES & NL

Ordinary Differential Equations and Dynamical Systems Book Review:

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.

Nonlinear Dynamics and Chaos

Nonlinear Dynamics and Chaos
Author: Steven H. Strogatz
Publsiher: CRC Press
Total Pages: 532
Release: 2018-05-04
ISBN 10: 0429972199
ISBN 13: 9780429972195
Language: EN, FR, DE, ES & NL

Nonlinear Dynamics and Chaos Book Review:

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields

Nonlinear Oscillations  Dynamical Systems  and Bifurcations of Vector Fields
Author: John Guckenheimer,Philip Holmes
Publsiher: Unknown
Total Pages: 484
Release: 2014-09-01
ISBN 10: 9781461211419
ISBN 13: 1461211417
Language: EN, FR, DE, ES & NL

Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields Book Review:

Normal Modes and Localization in Nonlinear Systems

Normal Modes and Localization in Nonlinear Systems
Author: Alexander F. Vakakis
Publsiher: Springer Science & Business Media
Total Pages: 294
Release: 2013-06-29
ISBN 10: 9401724520
ISBN 13: 9789401724524
Language: EN, FR, DE, ES & NL

Normal Modes and Localization in Nonlinear Systems Book Review:

The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape ¢n, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape ¢n. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996.

Qualitative Theory of Planar Differential Systems

Qualitative Theory of Planar Differential Systems
Author: Freddy Dumortier,Jaume Llibre,Joan C. Artés
Publsiher: Springer Science & Business Media
Total Pages: 302
Release: 2006-10-13
ISBN 10: 3540329021
ISBN 13: 9783540329022
Language: EN, FR, DE, ES & NL

Qualitative Theory of Planar Differential Systems Book Review:

This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.

Ordinary Differential Equations with Applications

Ordinary Differential Equations with Applications
Author: Carmen Chicone
Publsiher: Springer Science & Business Media
Total Pages: 636
Release: 2006-09-23
ISBN 10: 0387357947
ISBN 13: 9780387357942
Language: EN, FR, DE, ES & NL

Ordinary Differential Equations with Applications Book Review:

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
Publsiher: Springer Science & Business Media
Total Pages: 586
Release: 2013-03-19
ISBN 10: 0387217924
ISBN 13: 9780387217925
Language: EN, FR, DE, ES & NL

Introduction to Mechanics and Symmetry Book Review:

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.

Introduction to Asymptotic Methods

Introduction to Asymptotic Methods
Author: David Y. Gao,Vadim A. Krysko
Publsiher: CRC Press
Total Pages: 272
Release: 2006-05-03
ISBN 10: 1420011731
ISBN 13: 9781420011739
Language: EN, FR, DE, ES & NL

Introduction to Asymptotic Methods Book Review:

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m

Mechanics USA 1990

Mechanics USA 1990
Author: C. F. Chen,Chuan Fang Chen
Publsiher: Amer Society of Mechanical
Total Pages: 397
Release: 1990
ISBN 10: 9780791800133
ISBN 13: 079180013X
Language: EN, FR, DE, ES & NL

Mechanics USA 1990 Book Review:

Navier Stokes Equations

Navier Stokes Equations
Author: Roger Temam
Publsiher: American Mathematical Soc.
Total Pages: 408
Release: 2001-04-10
ISBN 10: 0821827375
ISBN 13: 9780821827376
Language: EN, FR, DE, ES & NL

Navier Stokes Equations Book Review:

Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.

Constructions of Strict Lyapunov Functions

Constructions of Strict Lyapunov Functions
Author: Michael Malisoff,Frédéric Mazenc
Publsiher: Springer Science & Business Media
Total Pages: 386
Release: 2009-06-13
ISBN 10: 1848825358
ISBN 13: 9781848825352
Language: EN, FR, DE, ES & NL

Constructions of Strict Lyapunov Functions Book Review:

Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed. This book contains a broad repertoire of Lyapunov constructions for nonlinear systems, focusing on methods for transforming non-strict Lyapunov functions into strict ones. Their explicitness and simplicity make them suitable for feedback design, and for quantifying the effects of uncertainty. Readers will benefit from the authors’ mathematical rigor and unifying, design-oriented approach, as well as the numerous worked examples.

Nonlinear Ordinary Differential Equations

Nonlinear Ordinary Differential Equations
Author: Dominic Jordan,Peter Smith
Publsiher: OUP Oxford
Total Pages: 540
Release: 2007-08-24
ISBN 10: 0191525995
ISBN 13: 9780191525995
Language: EN, FR, DE, ES & NL

Nonlinear Ordinary Differential Equations Book Review:

This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007). Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Differential Dynamical Systems Revised Edition

Differential Dynamical Systems  Revised Edition
Author: James D. Meiss
Publsiher: SIAM
Total Pages: 392
Release: 2017-01-24
ISBN 10: 161197464X
ISBN 13: 9781611974645
Language: EN, FR, DE, ES & NL

Differential Dynamical Systems Revised Edition Book Review:

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Bifurcation and Chaos in Nonsmooth Mechanical Systems

Bifurcation and Chaos in Nonsmooth Mechanical Systems
Author: Jan Awrejcewicz,Claude-Henri Lamarque
Publsiher: World Scientific
Total Pages: 543
Release: 2003
ISBN 10: 9812384596
ISBN 13: 9789812384591
Language: EN, FR, DE, ES & NL

Bifurcation and Chaos in Nonsmooth Mechanical Systems Book Review:

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
Publsiher: Springer Science & Business Media
Total Pages: 544
Release: 2013-06-29
ISBN 10: 9401587639
ISBN 13: 9789401587631
Language: EN, FR, DE, ES & NL

Nonlinear Oscillations and Waves in Dynamical Systems Book Review:

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.