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Friday, May 15, 2020 | History

4 edition of Nonlinear stability and bifurcation theory found in the catalog.

Nonlinear stability and bifurcation theory

an introduction for engineers and applied scientists

by H. Troger

  • 233 Want to read
  • 32 Currently reading

Published by Springer-Verlag in New York .
Written in English

    Subjects:
  • Differential equations, Nonlinear.,
  • Bifurcation theory.

  • Edition Notes

    Includes bibliographical references (p. 389-401) and index.

    StatementHans Troger, Alois Steindl.
    ContributionsSteindl, Alois, 1957-
    Classifications
    LC ClassificationsTA347.D45 T76 1991
    The Physical Object
    Paginationxi, 407 p. :
    Number of Pages407
    ID Numbers
    Open LibraryOL1545169M
    ISBN 100387822925, 3211822925
    LC Control Number91024316

      By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses.4/5(3). The generic case of stationary co-dimension-one bifurcation is a saddle-node is generic (that is, the probability is finite to pick a dynamical system having a saddle-node bifurcation) because fixed points lie on a smooth one-dimensional manifold in the combined space of phase space and control parameter. The minima and maxima of as a function of the curve length denote saddle. Nonlinearity, Bifurcation and Chaos - Theory and Application is an edited book focused on introducing both theoretical and application oriented approaches in science and engineering. It contains 12 chapters, and is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested Cited by: 6.   This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries. The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs).

      Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems. group theory, provides a powerful tool in gaining insight into the persistence of or change of the symmetry that a solution branch possesses at the bifurcation point. Singularity theory also concerns the stability of bifurcation solution branches. Often used is the so-called linear stability criterion. Under such a criterion. By providing an introduction to nonlinear differential equations, Dr. Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincaré-Bendixson theorem, the Hopf bifurcation and chaotic systems.5/5(1).

    In general, nonlinear problems in computational mechanics involve a number of parameters that influence the behavior of the physical system and that have to be taken into account in the computation. For example, in structural mechanics these parameters may characterize intrinsic quantities such as material properties, geometric dimensions, or.   The local bifurcation theory, taking up about half the book, depends on the breakdown of the implicit function theorem and is based on the Lyapunov-Schmidt reduction for infinite dimensional spaces. The case that the Fre´chet derivative has a one-dimensional kernel includes the saddle-node and the various types of pitchfork by: 8. Paul Glendinning's book has grown out of recurrent final-year undergraduate courses in nonlinear differential equations and bifurcation theory at Cambridge, while G. Nicolis's book derives from the lecture notes for a hour course about nonlinearity for scientists with a mathematical background.   Furthermore we introduce a nonlinearity relative to the saturation of the control force in the model, reduce the dynamics of the nonlinear map to its local center manifold, study the bifurcation along the stability border and identify conditions under which a supercritical or subcritical bifurcation by:


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Nonlinear stability and bifurcation theory by H. Troger Download PDF EPUB FB2

Nonlinear Stability and Bifurcation Theory An Introduction for Engineers and Applied Scientists. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. Nonlinear Stability and Bifurcation Theory Book Subtitle An Introduction for Engineers.

This was a good book. Ir was above my expertise but was instructive nonetheless. It covered the usual value of linearization. It also covered perturbation methods then bifurcation theory (saddlenode, transcritical, pitchfork and Hopf) and then discusses chaos through the horseshoe map by: @article{osti_, title = {Nonlinear stability and bifurcation theory}, author = {Troger, H and Steindl, A}, abstractNote = {There are now well over fifty books available on nonlinear science and chaos theory.

In the past year alone, six new technical journals appeared in these areas. (Some of them may even survive). Much of the activity has been in the physics and mathematics communities. Nonlinear Stability and Bifurcation Theory An Introduction Nonlinear stability and bifurcation theory book Engineers and Applied Scientists.

Authors (view affiliations) About this book. A Nonlinear stability and bifurcation theory book example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth.

This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and Cited by: The favorable reaction to the first edition of this book confirmed that the publication of such an application-oriented text on bifurcation theory of dynamical systems was well timed.

Nonlinear stability and bifurcation theory book The selected topics indeed cover ma-jor practical issues of applying the bifurcation theory to finite-dimensional problems. Nonlinear Differential Nonlinear stability and bifurcation theory book Invariance, Stability, and Bifurcation presents the developments in the qualitative theory of nonlinear differential equations.

This book discusses the exchange of mathematical ideas in stability and bifurcation theory. Organized into 26 chapters, this book begins with an overview of the initial value problem.

ISBN: OCLC Number: Description: xi, pages: illustrations ; 25 cm: Contents: 1 Introduction.- 2 Representation of systems.- Dynamical systems.- Time continuous system.- Time discrete system.- Statical systems.- Definitions of stability.- Stability in the sense of Ljapunov.- Structural stability.

In its most general form bifurcation theory is a theory of asymptotic solutions of nonlinear equations. By asymptotic solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of asymptotic.

This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems.

To begin with, bifurcation theory deals with the analysis of branch points of nonlinear functional equations in a vector space, usually a Banach space.

The subject of bifurcation is an important topic for applied mathematics in as much as it arises naturally in any physical system described by a nonlinear set of equations depending on a set of. This book covers solid mechanics for nonlinear elastic and elastoplastic materials, describing the behavior of ductile material subject to extreme mechanical loading and its eventual failure.

The book highlights constitutive features to describe the behavior of frictional materials such as geological media. On the basis of this theory, including large strain and inelastic behaviors.

This book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems.

Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. Get this from a library. Nonlinear solid mechanics: bifurcation theory and material instability. [Davide Bigoni] -- "This book covers solid mechanics for non-linear elastic and elastoplastic materials, describing the behaviour of ductile material subject to extreme mechanical loading and its eventual failure.

The. The purpose of the present chapter is once again to show on concrete new examples that chaos in one-dimensional unimodal mappings, dynamical chaos in systems of ordinary differential equations, diffusion chaos in systems of the equations with partial derivatives and chaos in Hamiltonian and conservative systems are generated by cascades of bifurcations under universal bifurcation Feigenbaum Cited by: 1.

The NOOK Book (eBook) of the Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability by Davide Bigoni at Barnes & Noble. FREE Shipping Due Author: Davide Bigoni. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in.

Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientists Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

Chaos theory is a branch of mathematics focusing on the study of chaos—states of dynamical systems whose apparently-random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of chaotic complex systems, there are underlying.

This book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential in order to understand the fascinating behavior of nonlinear discrete dynamical systems.

The theory is illuminated by several examples and exercises, many of them taken from population dynamical studies.

Bifurcation theory is the mathematical pdf of changes in the qualitative or topological structure of pdf given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation.Buy Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (Cambridge Texts in Applied Mathematics) by Glendinning, Paul (ISBN: ) from Amazon's Book Store.

Everyday low prices and free delivery on eligible orders/5(3).Nonlinear Systems: Analysis, Stability, and Ebook Bifurcation theory has been used to explain and understand the onset of fiutterin the dynamics of aircraft wing structures, the onset of oscillations in nonlinear circuits, surge and stall in aircraft engines, voltage collapse in a power transmission network.

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