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Calculating Branching Behavior of Boundary-Value Problems

  • Rüdiger Seydel
Chapter
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 5)

Abstract

The main topic of this chapter is the calculation of branching behavior of the one-parameter family of two-point boundary-value problems As usual, the variable y (t) consists of n scalar functions y 1 (t),…,y n (t). The right-hand side f(t, y, λ) is a vector function; the boundary conditions [the second equation (6.1)] consist of n scalar equations, The independent variable t (atb) need not be time; accordingly, the derivative with respect to t is denoted by a prime ′ rather than a dot: y′ = dy/dt. The bifurcation parameter λ can occur in the boundary conditions: However, because the methods discussed in this chapter are not affected by the dependence of r on λ, the notation r(y (a), y (b)) of equation (6.1) will be retained.

Keywords

Hopf Bifurcation Bifurcation Diagram Bifurcation Point Erential Equation Unstable Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnKölnGermany

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