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Journal ArticleDOI

Numerical computation of nonsimple turning points and cusps

Dirk Roose, +1 more
- 01 Jun 1985 - 
- Vol. 46, Iss: 2, pp 189-211
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TLDR
In this article, a method for the numerical computation of a double turning point corresponding to a cusp catastrophe of a nonlinear operator equation depending on two parameters is developed. But this method is limited to the finite-dimensional case.
Abstract: 
A method is developed for the numerical computation of a double turning point corresponding to a cusp catastrophe of a nonlinear operator equation depending on two parameters. An augmented system containing the original equation is introduced, for which the cusp point is an isolated solution. An efficient implementation of Newton's method in the finite-dimensional case is presented. Results are given for some chemical engineering problems and this direct method is compared with some other techniques to locate cusp points.

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Citations
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Journal ArticleDOI

Computing a closest bifurcation instability in multidimensional parameter space

Ian Dobson
- 01 Dec 1993 - 
TL;DR: In this paper, the authors proposed a method for computing the locally closest bifurcation to the nominal parameters of a stable equilibrium in a saddle-node or Hopf bifurbation.

Computation of cusp singularities for operator equations and their discretizations

Andreas Griewank, +1 more
TL;DR: In this article, the authors discuss the direct calculation of cusp singularities as solutions of a minimally augmented defining system, which is nonsingular under the canonical cusp conditions.
Journal ArticleDOI

Computation of cusp singularities for operator equations and their discretizations

Andreas Griewank, +1 more
- 01 Jun 1989 - 
Journal ArticleDOI

Numerical Methods for the Generalized Hopf Bifurcation

Willy Govaerts, +2 more
- 01 Jun 2000 - 
TL;DR: Two computational procedures are described, implemented in the software package content, to compute and numerically continue GH points, applied to a biochemical model and two examples from neurobiology.
Journal ArticleDOI

Computation of Singularities in Large Nonlinear Systems

Willy Govaerts
- 01 Jun 1997 - 
TL;DR: In this paper, a general approach for numerical computation of one-parameter singularities in the sense of Golubitsky and Schaeffer is proposed, where singularities of codimension three or less are organized in a new way.
References
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Book

Catastrophe theory and its applications

Timothy Poston, +2 more

Numerical solution of bifurcation and nonlinear eigenvalue problems.

Hb Keller
Journal ArticleDOI

The Calculation of Turning Points of Nonlinear Equations

G. Moore, +1 more
- 01 Aug 1980 - 
TL;DR: In this article, an enlarged system is introduced for which the turning point is a nonsingular solution and thus standard methods can be used to compute it, and numerical results for discretizations of a differential equation and an integral equation are given.
Journal ArticleDOI

Finite dimensional approximation of nonlinear problems

Franco Brezzi, +2 more
- 01 Feb 1981 - 
TL;DR: In this article, a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a Banach space has been studied, and general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point have been derived.
Journal ArticleDOI

A locally parameterized continuation process

Werner C. Rheinboldt, +1 more
- 01 Jun 1983 - 
TL;DR: The design of a package of continuation procedures called PITCON to handle the following tasks is described: follow numerically any a priori specified curve on an equilibrium manifold determine the exact location of target points where a given variable has a specified value.