Linearization and Transformation

David Betounes ()
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David Betounes: University of Southern Mississippi, Mathematics Department

Chapter Chapter 6 in Differential Equations: Theory and Applications, 2001, pp 231-274 from Springer

Abstract: Abstract In this chapter we present two basic techniques that are useful for analyzing nonlinear systems. One technique consists of linearizing about the fixed points to obtain local, qualitative pictures of the phase portrait via the corresponding linear systems. Thus, our previous work on linear systems has direct bearing on nonlinear systems. The validity of this technique is contained in the Linearization Theorem, which we present later on, after first applying it in numerous examples and exercises.

Keywords: Vector Field; Phase Portrait; Integral Curve; Polar System; Integral Curf (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-4971-7_6

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DOI: 10.1007/978-1-4757-4971-7_6

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