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Published in:
2010 | OriginalPaper | Chapter
Basic Nonlinear Phenomena
Author : Rüdiger Seydel
Published in: Practical Bifurcation and Stability Analysis
Publisher: Springer New York
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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.