Displaying similar documents to “Stable and unstable bifurcation in the von Kármán problem for a circular plate.”

Two-mode bifurcation in solution of a perturbed nonlinear fourth order differential equation

Ahmed Abbas Mizeal, Mudhir A. Abdul Hussain (2012)

Archivum Mathematicum

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In this paper, we are interested in the study of bifurcation solutions of nonlinear wave equation of elastic beams located on elastic foundations with small perturbation by using local method of Lyapunov-Schmidt.We showed that the bifurcation equation corresponding to the elastic beams equation is given by the nonlinear system of two equations. Also, we found the parameters equation of the Discriminant set of the specified problem as well as the bifurcation diagram.

One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

Borisov, Milen, Dimitrova, Neli (2010)

Serdica Journal of Computing

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This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities. * This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.

Bifurcation in the solution set of the von Kármán equations of an elastic disk lying on an elastic foundation

Joanna Janczewska (2001)

Annales Polonici Mathematici

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We investigate bifurcation in the solution set of the von Kármán equations on a disk Ω ⊂ ℝ² with two positive parameters α and β. The equations describe the behaviour of an elastic thin round plate lying on an elastic base under the action of a compressing force. The method of analysis is based on reducing the problem to an operator equation in real Banach spaces with a nonlinear Fredholm map F of index zero (to be defined later) that depends on the parameters α and β. Applying the implicit...