Stability of Linear Delay Differential Equations

A Numerical Approach with MATLAB

  • Dimitri Breda
  • Stefano Maset
  • Rossana Vermiglio

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Dimitri Breda, Stefano Maset, Rossana Vermiglio
    Pages 1-14
  3. Theory

    1. Front Matter
      Pages 15-16
    2. Dimitri Breda, Stefano Maset, Rossana Vermiglio
      Pages 17-21
    3. Dimitri Breda, Stefano Maset, Rossana Vermiglio
      Pages 23-33
    4. Dimitri Breda, Stefano Maset, Rossana Vermiglio
      Pages 35-41
  4. Numerical Analysis

    1. Front Matter
      Pages 43-44
    2. Dimitri Breda, Stefano Maset, Rossana Vermiglio
      Pages 45-65
    3. Dimitri Breda, Stefano Maset, Rossana Vermiglio
      Pages 67-86
  5. Implementation and Applications

    1. Front Matter
      Pages 87-87
    2. Dimitri Breda, Stefano Maset, Rossana Vermiglio
      Pages 89-116
    3. Dimitri Breda, Stefano Maset, Rossana Vermiglio
      Pages 117-145
  6. Back Matter
    Pages 147-158

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Dimitri Breda
    • 1
  • Stefano Maset
    • 2
  • Rossana Vermiglio
    • 3
  1. 1.Department of Mathematics and Computer ScienceUniversity of UdineUdineItaly
  2. 2.Department of Mathematics and GeosciencesUniversity of TriesteTriesteItaly
  3. 3.Department of Mathematics and Computer ScienceUniversity of UdineUdineItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-2107-2
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, New York, NY
  • eBook Packages Engineering
  • Print ISBN 978-1-4939-2106-5
  • Online ISBN 978-1-4939-2107-2
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • About this book
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