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Transcritical Bifurcation

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Bifurcation without Parameters

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

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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].

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References

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  5. Vanderbauwhede, A.: Centre manifolds, normal forms and elementary bifurcations. In: Kirchgraber, U., Walther, H.O. (eds.) Dynamics Reported 2, pp. 89–169. Teubner & Wiley, Stuttgart (1989)

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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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