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Article
Bifurcation of Solutions of Separable Parameterized Equations into Lines
Electronic Journal of Differential Equations
  • Tjalling J. Ypma, Western Washington University
  • Yun-Qiu Shen, Western Washington University
Document Type
Conference Proceeding
Publication Date
1-1-2010
Disciplines
Abstract

Many applications give rise to separable parameterized equations of the form A(y,µ)z + b(y, µ) = 0, where y Rn, z RN and the parameter µ R; here A(y,µ) is an (N + n) × N matrix and b(y, µ) RN +n. Under the assumption that A(y, µ) has full rank we showed in [21] that bifurcation points can be located by solving a reduced equation of the form f (y, µ) = 0. In this paper we extend that method to the case that A(y, µ) has rank deficiency one at the bifurcation point. At such a point the solution curve (y, µ, z) branches into infinitely many additional solutions,which form a straight line. A numerical method for reducing the problem to a smaller space and locating such a bifurcation point is given. Applications to equilibrium solutions of nonlinear ordinary equations and solutions of discretized partial differential equations are provided.

Required Publisher's Statement

Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations

This is an open access journal.

Comments

Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations

This is an open access journal.

Citation Information
Tjalling J. Ypma and Yun-Qiu Shen. "Bifurcation of Solutions of Separable Parameterized Equations into Lines" Electronic Journal of Differential Equations Vol. 19 (2010) p. 254 - 255
Available at: http://works.bepress.com/tjalling_ypma/11/