Titlebook: Elements of Applied Bifurcation Theory; Yuri A. Kuznetsov Book 2023Latest edition The Editor(s) (if applicable) and The Author(s), under e

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,Numerical Analysis ?of Bifurcations,l routines like those for solving linear systems, finding eigenvectors and eigenvalues, and performing numerical integration of ODEs are known to the reader. Instead, we focus on algorithms that are more specific to bifurcation analysis, specifically those for the location?of equilibria (fixed point

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,Kontrast und Signal-zu-Rausch-Verh?ltnis,This chapter introduces some basic terminology. First, we define a . and give several examples, including symbolic dynamics. Then we introduce the notions of ., and their .. As we shall see while analyzing the ., invariant sets can have very complex structures.

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https://doi.org/10.1007/978-3-642-66120-4The list of possible bifurcations in multidimensional systems is not exhausted by those studied in the previous chapters. Actually, even the complete list of all generic one-parameter bifurcations is unknown.

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One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems,In this chapter, which is organized very much like Chap. 3, we present bifurcation conditions defining the simplest bifurcations of fixed points in .-dimensional discrete-time dynamical systems: the fold, the flip, and the Neimark-Sacker bifurcations.

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