Linearization and Transformation

  • David Betounes


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.


Vector Field Phase Portrait Integral Curve Polar System Integral Curf 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • David Betounes
    • 1
  1. 1.Mathematics DepartmentUniversity of Southern MississippiHattiesburgUSA

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