Abstract
Ordinary differential equations are the backbone of this book. Symbolically this class of problems can be represented by the ODE prototype equation which is a short way for with f sufficiently smooth. For this type of equation we discuss parameter dependence, bifurcation, and stability in detail. Many other bifurcation problems are not of this ODE type. For example, a delay may be involved, or the dynamics fails to be smooth. But even then the ODE background is helpful. On the one hand, methods can be applied that are similar as the ODE approaches. On the other hand, the ODE system (3.1) can be used to approximate non-ODE situations, or to characterize certain special cases.
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© 2010 Springer Science+Business Media, LLC
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Seydel, R. (2010). Applications and Extensions. In: Practical Bifurcation and Stability Analysis. Interdisciplinary Applied Mathematics, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1740-9_3
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DOI: https://doi.org/10.1007/978-1-4419-1740-9_3
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1739-3
Online ISBN: 978-1-4419-1740-9
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