Stability of Linear Delay Differential Equations (eBook)
XI, 158 Seiten
Springer New York (Verlag)
978-1-4939-2107-2 (ISBN)
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.
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.
Erscheint lt. Verlag | 21.10.2014 |
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Reihe/Serie | SpringerBriefs in Control, Automation and Robotics | SpringerBriefs in Electrical and Computer Engineering |
Zusatzinfo | XI, 158 p. 25 illus., 1 illus. in color. |
Verlagsort | New York |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
Mathematik / Informatik ► Mathematik ► Analysis | |
Naturwissenschaften | |
Technik ► Elektrotechnik / Energietechnik | |
Schlagworte | asymptotic stability • Characteristic Equation, Roots and Multipliers • Equilibria and Periodic Solutions • infinite dimensional dynamical systems • Matlab Codes • Numerical Stability Analysis • Pseudospectral and Collocation Methods • Retarded Functional and Delay Differential Equations • Semigroup of Solution Operators and Infinitesimal Generator • Spectrum of Linear Operators and Eigenvalue Problems • Time-delay models |
ISBN-10 | 1-4939-2107-X / 149392107X |
ISBN-13 | 978-1-4939-2107-2 / 9781493921072 |
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