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Basic Nonlinear Phenomena

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

Abstract

Beginning with this chapter, nonlinearity and parameter dependence willplay a crucial role. We shall assume throughout that λ is a real parameter, and we shall study solutions of a system of ODEs, or solutions of a system of “algebraic” equations, Sometimes boundary conditions must be attached to equation (2.1). As in Chapter 1, the vectors y and f have n components. If a particular example involves more than one parameter, we assume for the time being that all except λ are kept fixed. Clearly, solutions y of equation (2.1) or (2.2) in general vary with λ. We shall assume throughout that f depends smoothly on y and λ—that is, f is to be sufficiently often continuously differentiable. This hypothesis is usually met by practical examples.

Keywords

Periodic Orbit Hopf Bifurcation Bifurcation Diagram Bifurcation Point Homoclinic Orbit 
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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