Stability of Linear Delay Differential Equations

A Numerical Approach with MATLAB

Dimitri Breda, Stefano Maset, Rossana Vermiglio (Autoren)

Buch | Softcover

158 Seiten

2014 | 2015 ed.
Springer-Verlag New York Inc.
978-1-4939-2106-5 (ISBN)

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This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.

Introduction.- Part I: Theory.- Notation and basics.- Stability of linear autonomous equations.- Stability of linear periodic equations.- Part II: Numerical Analysis.- The infinitesimal generator approach.- The solution operator approach.- Part III: Implementation and applications.- MATLAB implementation.- Applications.

Reihe/Serie	SpringerBriefs in Control, Automation and Robotics
Reihe/Serie	SpringerBriefs in Electrical and Computer Engineering
Zusatzinfo	1 Illustrations, color; 24 Illustrations, black and white
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Technik ► Elektrotechnik / Energietechnik
Schlagworte	asymptotic stability • Delay differential equations • Differenzialgleichungen • Discretized solution operator • Equilibria in population dynamics • Floquet theory • MATLAB (Software) • Numerische Analysis • Pseudospectral methods
ISBN-10	1-4939-2106-1 / 1493921061
ISBN-13	978-1-4939-2106-5 / 9781493921065
Zustand	Neuware