research-article

Singular Perturbations of Bifurcations with Multiple Independent Bifurcation Parameters

Author:

Robert W. KolkkaAuthors Info & Claims

SIAM Journal on Applied Mathematics, Volume 44, Issue 2

Pages 257 - 269

https://doi.org/10.1137/0144019

Published: 01 April 1984 Publication History

Abstract

There are several nonlinear bifurcation problems which involve multiple bifurcation parameters (“specified inputs”). Often there is a corresponding “perturbed” problem associated with the bifurcation problem which models imperfections. Instead of bifurcation, the perturbed problem exhibits a smooth but rapid transition in the critical range of the bifurcation parameter. A new generalization of the single bifurcation parameter method of Matkowsky and Reiss, SPB (“Singular Perturbations of Bifurcations”) [SIAM J. Appl. Math., 33 (1977), pp. 230–255] is employed to solve the problem of the slightly crooked rotating elastica (shaft) subject to a dead load applied at the ends.

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Bernard J. Matkowsky, Edward L. Reiss, Singular perturbations of bifurcations, SIAM J. Appl. Math., 33 (1977), 230–255

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Index Terms

Singular Perturbations of Bifurcations with Multiple Independent Bifurcation Parameters
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Numerical analysis
      1. Numerical differentiation

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Applied Mathematics

SIAM Journal on Applied Mathematics Volume 44, Issue 2

Apr 1984

230 pages

ISSN:0036-1399

DOI:10.1137/smjmap.1984.44.issue-2

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Society for Industrial and Applied Mathematics

United States

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Published: 01 April 1984

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Abstract

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Recommendations

Singular Homoclinic Bifurcations in a Planar Fast-Slow System

A complete bifurcation diagram of nonlocal bifurcations of singular points in the Lorenz system

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