Titlebook: Bifurcation without Parameters; Stefan Liebscher Book 2015 The Editor(s) (if applicable) and The Author(s), under exclusive license to Spr

GLIDE

消極詞匯

Alec A. Macaulay MD,Jeremy T. Smith MD. At isolated points, one of the non-degeneracy conditions?(4.8,?4.9) may fail and codimension-two singularities appear. We shall discuss these degeneracies, first in a one-parameter-family of lines of equilibria and then along a two-dimensional equilibrium surface.

spinal-stenosis

Puncture of gynecological masses,sverse to a plane of equilibria. It turns out that instead we can study a one-parameter family of lines in a system depending on one parameter. Indeed, the rescaled normal form?(11.6) is the same in both cases.

淘氣

珊瑚

Novel Drugs in the Treatment of HypertensionThis chapter introduces the setting in which we shall study bifurcations without parameters. We compare it with classical bifurcation theory and give an overview and classification of the results presented in the following chapters.

除草劑

Pheochromocytoma/ParagangliomasCosymmetries have been introduced by Yudovich and Kurakin to study limit cycles near manifolds of equilibria via Lyapunov-Schmidt reduction [49, 50]. They turn out to be equivalent to the existence of manifolds of equilibria, provided some non-degeneracy conditions are satisfied.

Dictation

https://doi.org/10.1007/978-1-84800-395-8In 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].

合并

Percutaneous Mechanical Assist Devices,Without parameters, no periodic orbits bifurcate. Depending on the drift condition, two cases appear. Both are discussed in this chapter.

Crohns-disease

Maxwell Sehested,Niels Juul,Bo HainauIn this chapter we study the Poincaré-Andronov-Hopf bifurcation without parameters, see Chap.?., with an additional degeneracy of the drift or transversality due to an additional parameter or an additional dimension of the primary manifold of equilibria.

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