Abstract
In this chapter, which is organized very much like Chapter 3, we present bifurcation conditions defining the simplest bifurcations of fixed points in n-dimensional discrete-time dynamical systems: the fold, the flip, and the Neimark-Sacker bifurcations. Then we study these bifurcations in the lowest possible dimension in which they can occur: the fold and flip bifurcations for scalar systems and the Neimark-Sacker bifurcation for planar systems. In Chapter 5 it will be shown how to apply these results to n-dimensional systems when n is larger than one or two, respectively.
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Kuznetsov, Y.A. (2004). One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems. In: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol 112. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3978-7_4
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DOI: https://doi.org/10.1007/978-1-4757-3978-7_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1951-9
Online ISBN: 978-1-4757-3978-7
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