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Shape, smoothness, and invariant stratification of an attracting set for delayed monotone positive feedback

Author: Tibor Krisztin; Hans-Otto Walther; Jianhong Wu
Publisher: Providence, R.I. : American Mathematical Society, 1999.
Series: Fields Institute monographs, 11.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Contains results about the global dynamics defined by a class of delay differential equations which model basic feedback mechanisms and arise in a variety of applications such as neural networks.  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Tibor Krisztin; Hans-Otto Walther; Jianhong Wu
ISBN: 082181074X 9780821810743
OCLC Number: 39860110
Description: vii, 245 pages ; 27 cm.
Contents: Introduction The delay differential equation and the hypotheses The separatrix The leading unstable set of the origin Oscillation frequencies Graph representations Dynamics on $\overline W$ and disk representation of $\overline W \cap S$ Minimal linear instability of the periodic orbit $\mathcal O$ Smoothness of $W \cap S$ in case $\mathcal O$ is hyperbolic Smoothness of $W \cap S$ in case $\mathcal O$ is not hyperbolic The unstable set of $\mathcal O$ contains the nonstationary points of bd$W$ bd$W$ contains the unstable set of the periodic orbit $\mathcal O$ $H \cap \overline W$ is smooth near $p_0$ Smoothness of $\overline W$, bd$W$ and $\overline W \cap S$ Homeomorphisms from bd$W$ onto the sphere and the cylinder Homeomorphisms from $\overline W$ onto the closed ball and the solid cylinder Resume Equivalent norms, invariant manifolds, Poincare maps and asymptotic phases Smooth center-stable manifolds for $C^1$-maps Smooth generalized center-unstable manifolds for $C^1$-maps Invariant cones close to neutrally stable fixed points with 1-dimensional center spaces Unstable sets of periodic orbits A discrete Lyapunov functional and a-priori estimates Floquet multipliers for a class of linear periodic delay differential equations Some results from topology Bibliography Index.
Series Title: Fields Institute monographs, 11.
Responsibility: Tibor Krisztin, Hans-Otto Walther, Jianhong Wu.

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