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Transcritical Bifurcation

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2117)

Abstract

In this chapter we study the simplest bifurcation without parameters: a line of equilibria which loses normal stability when a simple eigenvalue crosses zero transversely. This case has already been studied in [52], see also [28].

Keywords

  • Normal Form
  • Center Manifold
  • Eigenvalue Zero
  • Jordan Block
  • Pitchfork Bifurcation

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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Fig. 4.1
Fig. 4.2
Fig. 4.3

References

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Liebscher, S. (2015). Transcritical Bifurcation. In: Bifurcation without Parameters. Lecture Notes in Mathematics, vol 2117. Springer, Cham. https://doi.org/10.1007/978-3-319-10777-6_4

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