Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback (Fields Institute Monographs, 11)

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9780821810743: Shape, Smoothness and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback (Fields Institute Monographs, 11)

This book contains recent 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. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlling the growth and decay of solutions with prescribed oscillation frequency, a discrete Lyapunov functional counting zeros, methods to represent invariant sets as graphs, and Poincare-Bendixson techniques for classes of delay differential systems. Several appendices provide the general results needed in the case study, so the presentation is self-contained. Some of the general results are not available elsewhere, specifically on smooth infinite-dimensional center-stable manifolds for maps. Results in the appendices will be useful for future studies of more complicated attractors of delay and partial differential equations.

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Tibor Krisztin, Hans-Otto Walther, Jianhong Wu
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Book Description American Mathematical Society, United States, 1998. Hardback. Book Condition: New. Language: English . Brand New Book. This book contains recent 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. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlling the growth and decay of solutions with prescribed oscillation frequency, a discrete Lyapunov functional counting zeros, methods to represent invariant sets as graphs, and Poincare-Bendixson techniques for classes of delay differential systems.Several appendices provide the general results needed in the case study, so the presentation is self-contained. Some of the general results are not available elsewhere, specifically on smooth infinite-dimensional center-stable manifolds for maps. Results in the appendices will be useful for future studies of more complicated attractors of delay and partial differential equations. Bookseller Inventory # AAN9780821810743

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Tibor Krisztin
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Book Description American Mathematical Society, 1998. HRD. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # CE-9780821810743

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Tibor Krisztin, Hans-Otto Walther, Jianhong Wu
Published by American Mathematical Society, United States (1998)
ISBN 10: 082181074X ISBN 13: 9780821810743
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Book Description American Mathematical Society, United States, 1998. Hardback. Book Condition: New. Language: English . Brand New Book. This book contains recent 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. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlling the growth and decay of solutions with prescribed oscillation frequency, a discrete Lyapunov functional counting zeros, methods to represent invariant sets as graphs, and Poincare-Bendixson techniques for classes of delay differential systems.Several appendices provide the general results needed in the case study, so the presentation is self-contained. Some of the general results are not available elsewhere, specifically on smooth infinite-dimensional center-stable manifolds for maps. Results in the appendices will be useful for future studies of more complicated attractors of delay and partial differential equations. Bookseller Inventory # AAN9780821810743

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Hans-Otto Walther, and Jianhong Wu Tibor Krisztin
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Book Description American Mathematical Society, Fields Institute, 1998. Hardcover. Book Condition: New. book. Bookseller Inventory # M082181074X

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Krisztin, Tibor/ Walther, Hans-Otto/ Wu, Jianhong
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Book Description Amer Mathematical Society, 1998. Hardcover. Book Condition: Brand New. first edition edition. 245 pages. 10.50x7.25x0.75 inches. In Stock. Bookseller Inventory # __082181074X

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