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Thursday, May 14, 2020 | History

7 edition of The Hopf bifurcation and its applications found in the catalog.

The Hopf bifurcation and its applications

by Jerrold E. Marsden

  • 70 Want to read
  • 7 Currently reading

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

    Subjects:
  • Differential equations.,
  • Differential equations, Partial.,
  • Differentiable dynamical systems.,
  • Stability.

  • Edition Notes

    StatementJ. E. Marsden and M. McCracken, with contributions by P. Chernoff ... [et al.].
    SeriesApplied mathematical sciences ;, v. 19, Applied mathematical sciences (Springer-Verlag New York Inc.) ;, v. 19.
    ContributionsMcCracken, Marjorie, 1949- joint author.
    Classifications
    LC ClassificationsQA1 .A647 vol. 19, QA372 .A647 vol. 19
    The Physical Object
    Paginationxiii, 408 p. :
    Number of Pages408
    ID Numbers
    Open LibraryOL4890021M
    ISBN 100387902007
    LC Control Number76021727

    We state conditions for Hopf bifurcation, i.e., for existence, local uniqueness (up to phase shifts), smoothness and smooth dependence on lambda of time-periodic solutions bifurcating from the. () Poincaré–Andronov–Hopf Bifurcation and the Local Hilbert’s 16th Problem. Qualitative Theory of Dynamical Systems , () Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a cubic Lyapunov by:

    Hopf bifurcation and Turing instability in the reaction–diffusion In his book, Murray () studied the () for a recent survey on abstract bifurcation theorems and applications to spatiotemporal models from ecology and biochemistry. In this article, we analyse the stability and Hopf bifurcation of the positive equilibrium in both. where is a smooth function. Suppose that at, the system (a1) has an equilibrium position with a simple pair of purely imaginary eigenvalues,, of its Jacobian , generically, a unique limit cycle bifurcates from the equilibrium while it changes stability, as passes phenomenon is called the Hopf (or Andronov–Hopf) bifurcation.

    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. The selected topics indeed cover ma-jor practical issues of applying the bifurcation theory to finite-dimensional problems. Machine derived contents note: 1. The Hopf Bifurcation Theorum; 2. Applications: Ordinary Differential Equations (by hand); 3. Numerical Evaluation of Hopf Bifurcation Formulae; 4. Applications: Differential-Difference and Integro-differential Equations (by hand); 5. Applications: Partial Differential Equations (by hand). Notes.


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The Hopf bifurcation and its applications by Jerrold E. Marsden Download PDF EPUB FB2

The Hopf Bifurcation and Its Applications (Applied Mathematical Sciences) 1st Edition by J. Marsden (Author)Cited by: The Hopf Bifurcation and Its Applications.

Usually dispatched within 3 to 5 business days. The goal of these notes is to give a reasonahly com­ plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe­ cific problems, including stability : Springer-Verlag New York.

referred to as the Hopf bifurcation with applications to spe­ cific problems, including stability calculations. Historical­ ly, the subject had its origins in the works of Poincare [1] around and was extensively discussed by Andronov and Witt [1] and their co-workers starting around Hopf's basic paper [1] The Hopf bifurcation and its applications book in Introduction.

The goal of these notes is to give a reasonahly com­ plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe­ cific problems, including stability calculations. Historical­ ly, the subject had its origins in the works of Poincare [1] around and was extensively discussed by Andronov and Witt [1] and their co-workers starting.

The Hopf Bifurcation and Its Applications. | J. Marsden, M. McCracken | download | B–OK. Download books for free. Find books. The Hopf Bifurcation and Its Applications (Applied Mathematical Sciences No) Marsden, J.

E.; McCracken, M. Published by Springer Verlag, U.S.A. For other applications and related topics, we refer to the monographs of Andronov and Chaiken [1], Minorsky [1] and Thom [1]. The Hopf bifurcation refers to the development of periodic orbits ("self-oscillations") from a stable fixed point, as a parameter crosses a critical by: Hopf bifurcation and its applications.

New York: Springer-Verlag, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Jerrold E Marsden; Marjorie McCracken.

is a platform for academics to share research papers. The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems Abstract: One of the most powerful methods for studying periodic solutions In autonomous nonlinear systems is the theory which has developed from a proof by by: The Hopf Bifurcation and Its Applications - free book at E-Books Directory.

You can download the book or read it online. It is made freely available by its author and publisher. Theory And Application Of Hopf Bifurcation book. Read reviews from world’s largest community for readers.

The Hopf Bifurcation' describes a phenomenon th /5. The `Hopf Bifurcation' describes a phenomenon that occurs widely in nature: the birth of a family of oscillations as a controlling parameter is varied. In a control system consisting of an engine with a centrifugal governor, for example, when the amount of damping associated with the governor is decreased, oscillations can arise, which may Author: B.

Hassard, N. Kazarinoff, Y.-H. Wan. The `Hopf Bifurcation' describes a phenomenon that occurs widely in nature: the birth of a family of oscillations as a controlling parameter is varied.

In a control system consisting of an engine with a centrifugal governor, for example, when the amount of damping associated with the governor is decreased, oscillations can arise, which may significantly disturb normal operation of the engine.

In this paper, we consider the Turing–Hopf bifurcation arising from the reaction–diffusion equations. It is a degenerate case and where the characteristic equation has a Cited by: The Hopf Bifurcation and Its Applications (Applied Mathematical Sciences) by J.

Marsden. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Bifurcation Analysis and Its Applications 5 and dropping higher order terms, we obtain f(x) ≈ f(x¯)ε(t). Note that dropping these higher order terms is valid since ε(t) substituting x(t)= x¯ +ε(t) into the LHS of the ODE, ε(t)=f(x¯)ε(t).

The goal is to determine if we have growing or decaying solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references.

Contents: Introduction; The Hopf Bifurcation. Book Reviews. The Hopf Bifurcation and Its Applications. Marsden, Author, J. Marsden, Author Two-Dimension Simulation of a Red Blood Cell Partitioning in Microvascular Bifurcation. International Conference on Software Technology and Engineering (ICSTE )Cited by:.

Abstract. The method of averaging* provides an algorithm for preparing a bifurcation problem, that is, putting it into a normal form. Once this is done, one may more readily determine certain qualitative features of the bifurcation, by means of the implicit function theorem (or contraction mapping principle) and the center manifold by: 1.Hopf Bifurcation and its Applications, () by J Marsden, M McCracken Add To MetaCart.

Tools. Sorted by: Results 1 - 10 of Next 10 → Nonlinear stability of fluid and plasma equilibria by Hopf and steady state bifurcation analysis are carried out in details. In particular we show the existence of multiple spatially non-homogeneous.5.

Applications: Partial Differential Equations (by hand). (source: Nielsen Book Data) Summary The 'Hopf Bifurcation' describes a phenomenon that occurs widely in nature: the birth of a family of oscillations as a controlling parameter is varied.