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    Introduction to bifurcation-theory

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    Crawford_1991.pdf (2.778Mb)
    Date
    1991-10
    Author
    Crawford, J. D.
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    Abstract
    The theory of bifurcation from equilibria based on center-manifold reductio, and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail: a Hopf bifurcation occurring in a model of three-wave mode coupling and steady-state bifurcations occurring in the real Landau-Ginzburg equation. The former provides an example of the importance of degenerate bifurcations in problems with more than one parameter and the latter illustrates new effects introduced into a bifurcation problem by a continuous symmetry.
    Department
    Physics
    Subject
    non-linear transformations
    eckhaus instability
    symmetry
    convection
    turbulence
    stability
    patterns
    behavior
    systems
    orbits
    URI
    http://hdl.handle.net/2152/61063
    xmlui.dri2xhtml.METS-1.0.item-citation
    Crawford, John David. "Introduction to bifurcation theory." Reviews of Modern Physics 63, no. 4 (1991): 991.
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    • facebook
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    © The University of Texas at Austin