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A note on Computing simple bifurcation points

Bemerkungen zur Berechnung einfacher Bifurkationspunkte

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A direct method computing simple bifurcation points or isola formation centres is suggested. It is based on an improved implementation of the method published in Computing 35, 277–294 (1985) by G. Pönisch.


Es wird ein direktes Verfahren zur Berechnung einfacher Bifurkationspunkte bzw. von Einsiedlerpunkten vorgeschlagen, das auf einer verbesserten Implementierung eines von G. Pönisch in Computing 35, 277–294 (1985) veröffentlichten Verfahrens beruht.

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  1. [1]

    Crandall, M. C., Rabinowitz, P. H.: Bifurcation from simple eigenvalues. J. Funct. Anal.8, 321–340 (1971).

  2. [2]

    Golubitsky, M., Schaeffer, D. G.: Singularities and Groups in Bifurcation Theory (Volume 1). Berlin-Heidelberg-New York: Springer, 1985.

  3. [3]

    Griewank, A., Reddien, G. W.: Characterisation and computation of generalized turning points. SIAM J. Numer. Anal.21, 176–185 (1984).

  4. [4]

    Janovsky, V.: Minimally extended defining conditions for singularities of codim ≤2. Numer. Funct. Anal. Optimiz.9 (11–12), 1309–1349 (1987–88).

  5. [5]

    Jepson, A. D., Spence, A.: Singular points and their computation. In: Numerical Methods for Bifurcation Problems (Küpper, T., Mittlemann, H. D., Weber, H., eds.), pp. 195–209 (ISNM-70). Basel: Birkhäuser 1984.

  6. [6]

    Menzel, R., Pönisch, G.: A quadratically convergent method for computing simple singular roots and its application to determining simple bifurcation points. Computing32, 127–138 (1984).

  7. [7]

    Mittlemann, H. D., Weber, H.: Numerical methods for bifurcation problems—a surway and classification. In: Bifurcation Problems and Their Numerical Solution (Mittlemann, H. D., Weber, H., eds.), pp. 1–45 (ISNM 54), Basel: Birkhäuser 1980.

  8. [8]

    Moore, G.: The numerical treatment of nontrivial bifurcation points. Numer. Funct. Anal. Optimiz. 2, 441–472 (1980).

  9. [9]

    Pönisch, G.: Computing simple bifurcation points using a minimally extended system of nonlinear equations. Computing35, 277–294 (1985).

  10. [10]

    Seydel, R.: Numerical computation of branch points in nonlinear equations. Numer. Math.33, 339–352 (1979).

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Janovský, V. A note on Computing simple bifurcation points. Computing 43, 27–36 (1989). https://doi.org/10.1007/BF02243803

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AMS Subject Classification

  • Primary 65H
  • Secondary 47E

Key words

  • Nonlinear parameter-dependent equations
  • bifurcation points
  • Newton-like method