Poincar   Andronov Melnikov Analysis for Non Smooth Systems Book

Poincar Andronov Melnikov Analysis for Non Smooth Systems


  • Author : Michal Fečkan
  • Publisher : Academic Press
  • Release Date : 2016-06-07
  • Genre: Mathematics
  • Pages : 260
  • ISBN 10 : 9780128043646

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Poincar Andronov Melnikov Analysis for Non Smooth Systems Excerpt :

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 Book

Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts


  • Author : Olejnik Pawel
  • Publisher : #N/A
  • Release Date : 2017-07-07
  • Genre: Mathematics
  • Pages : 276
  • ISBN 10 : 9789813225305

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Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts Excerpt :

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 Book

Mathematical Modelling in Health Social and Applied Sciences


  • Author : Hemen Dutta
  • Publisher : Springer Nature
  • Release Date : 2020-02-29
  • Genre: Mathematics
  • Pages : 320
  • ISBN 10 : 9789811522864

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Mathematical Modelling in Health Social and Applied Sciences Excerpt :

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 Book

Elements of Applied Bifurcation Theory


  • Author : Yuri Kuznetsov
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Mathematics
  • Pages : 632
  • ISBN 10 : 9781475739787

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Elements of Applied Bifurcation Theory Excerpt :

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 Book

Mathematical Reviews


  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2000
  • Genre: Mathematics
  • Pages : null
  • ISBN 10 : UVA:X006089013

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Mathematical Reviews Excerpt :

Ordinary Differential Equations and Dynamical Systems Book

Ordinary Differential Equations and Dynamical Systems


  • Author : Gerald Teschl
  • Publisher : American Mathematical Soc.
  • Release Date : 2012-08-30
  • Genre: Mathematics
  • Pages : 356
  • ISBN 10 : 9780821883280

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Ordinary Differential Equations and Dynamical Systems Excerpt :

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 Book

Nonlinear Dynamics and Chaos


  • Author : Steven H. Strogatz
  • Publisher : CRC Press
  • Release Date : 2018-05-04
  • Genre: Mathematics
  • Pages : 532
  • ISBN 10 : 9780429972195

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Nonlinear Dynamics and Chaos Excerpt :

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.

Mechanics USA 1990 Book

Mechanics USA 1990


  • Author : C. F. Chen
  • Publisher : Amer Society of Mechanical
  • Release Date : 1990
  • Genre: Science
  • Pages : 412
  • ISBN 10 : 079180013X

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Introduction to Asymptotic Methods Book

Introduction to Asymptotic Methods


  • Author : David Y. Gao
  • Publisher : CRC Press
  • Release Date : 2006-05-03
  • Genre: Mathematics
  • Pages : 272
  • ISBN 10 : 9781420011739

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Introduction to Asymptotic Methods Excerpt :

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

Ordinary Differential Equations with Applications Book

Ordinary Differential Equations with Applications


  • Author : Carmen Chicone
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-09-23
  • Genre: Mathematics
  • Pages : 636
  • ISBN 10 : 9780387357942

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Ordinary Differential Equations with Applications Excerpt :

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.

Navier Stokes Equations Book

Navier Stokes Equations


  • Author : Roger Temam
  • Publisher : American Mathematical Soc.
  • Release Date : 2001-04-10
  • Genre: Mathematics
  • Pages : 408
  • ISBN 10 : 9780821827376

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Navier Stokes Equations Excerpt :

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.

Nonlinear Oscillations and Waves in Dynamical Systems Book

Nonlinear Oscillations and Waves in Dynamical Systems


  • Author : P.S Landa
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Mathematics
  • Pages : 544
  • ISBN 10 : 9789401587631

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Nonlinear Oscillations and Waves in Dynamical Systems Excerpt :

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.

Qualitative Theory of Planar Differential Systems Book

Qualitative Theory of Planar Differential Systems


  • Author : Freddy Dumortier
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-10-13
  • Genre: Mathematics
  • Pages : 302
  • ISBN 10 : 9783540329022

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Qualitative Theory of Planar Differential Systems Excerpt :

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.