Shape, smoothness, and invariant stratification of an attracting set for delayed monotone positive feedback / Tibor Krisztin, Hans-Otto Walther, Jianhong Wu.

Format:

Book

Author/Creator:

Krisztin, Tibor, 1956- author.

Contributor:

Walther, Hans-Otto.

Wu, Jianhong.

Series:

Fields Institute Monographs, 2472-4173 ; v. 11

Language:

English

Subjects (All):

Delay differential equations--Numerical solutions.

Delay differential equations.

Initial value problems.

Attractors (Mathematics).

Physical Description:

1 online resource (vii, 245 pages)

Place of Publication:

Providence, R.I. : American Mathematical Society, 1999.

System Details:

Mode of access : World Wide Web

Contents:

Chapter 1. Introduction Chapter 2. The delay differential equation and the hypotheses Chapter 3. The separatrix Chapter 4. The leading unstable set of the origin Chapter 5. Oscillation frequencies Chapter 6. Graph representations Chapter 7. Dynamics on $\overline W$ and disk representation of $\overline W \cap S$ Chapter 8. Minimal linear instability of the periodic orbit $\mathcal O$ Chapter 9. Smoothness of $W \cap S$ in case $\mathcal O$ is hyperbolic Chapter 10. Smoothness of $W \cap S$ in case $\mathcal O$ is not hyperbolic Chapter 11. The unstable set of $\mathcal O$ contains the nonstationary points of bd$W$ Chapter 12. bd$W$ contains the unstable set of the periodic orbit $\mathcal O$ Chapter 13. $H \cap \overline W$ is smooth near $p_0$ Chapter 14. Smoothness of $\overline W$, bd$W$ and $\overline W \cap S$ Chapter 15. Homeomorphisms from bd$W$ onto the sphere and the cylinder Chapter 16. Homeomorphisms from $\overline W$ onto the closed ball and the solid cylinder Chapter 17. Resumé Appendix I. Equivalent norms, invariant manifolds, Poincaré maps and asymptotic phases Appendix II. Smooth center-stable manifolds for $C^1$-maps Appendix III. Smooth generalized center-unstable manifolds for $C^1$-maps Appendix IV. Invariant cones close to neutrally stable fixed points with 1-dimensional center spaces Appendix V. Unstable sets of periodic orbits Appendix VI. A discrete Lyapunov functional and a-priori estimates Appendix VII. Floquet multipliers for a class of linear periodic delay differential equations Appendix VIII. Some results from topology

Notes:

Includes bibliographical references (pages 239-241) and index.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Description based on print version record.

Other Format:

Print version: Krisztin, Tibor, 1956- Shape, smoothness, and invariant stratification of an attracting set for delayed monotone positive feedback /

ISBN:

9781470431389 (online)

Access Restriction:

Restricted for use by site license.