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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W. Schlegel,L. R. Schad,K. K. Herfarthl systems and their classification, bifurcations and bifurcation diagrams, and topological normal forms for bifurcations. The last section is devoted to the more abstract notion of structural stability. In this chapter we will be dealing only with dynamical systems in the state space .. We would lik

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Maximilian Reiser,Wolfhard Semmleropf bifurcations. Then we study these bifurcations in the lowest possible dimensions: the fold bifurcation for scalar systems and the Hopf bifurcation for planar systems. Appendixes A and B are devoted to technical questions appearing in the analysis of Hopf bifurcation: Effects of higher-order term

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Anatomisch-funktionelle Grundlagen,e dynamical systems. First, we consider in detail two- and three-dimensional cases where geometrical intuition can be fully exploited. Then we show how to reduce generic .-dimensional cases to the considered ones plus a four-dimensional case treated in Appendix A.

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Vollendete Werke vor der ,: ,, Frühe Liederr the final two bifurcations in the previous chapter, the description of the majority of these bifurcations is incomplete in principle. For all but two cases, only . normal forms can be constructed. Some of these normal forms will be presented in terms of associated planar continuous-time systems wh

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https://doi.org/10.1007/978-3-476-02910-2l 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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Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria,e dynamical systems. First, we consider in detail two- and three-dimensional cases where geometrical intuition can be fully exploited. Then we show how to reduce generic .-dimensional cases to the considered ones plus a four-dimensional case treated in Appendix A.

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Yuri A. KuznetsovCenter manifold reduction & computation of normal forms is applied; normal forms for bifurcations of limit cycles.More results on topological equivalence of scalar maps are given.Techniques to study d