Discrete Dynamical Models

  • Ernesto Salinelli
  • Franco Tomarelli

Part of the UNITEXT book series (UNITEXT, volume 76)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 76)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Ernesto Salinelli, Franco Tomarelli
    Pages 1-23
  3. Ernesto Salinelli, Franco Tomarelli
    Pages 25-83
  4. Ernesto Salinelli, Franco Tomarelli
    Pages 85-124
  5. Ernesto Salinelli, Franco Tomarelli
    Pages 125-177
  6. Ernesto Salinelli, Franco Tomarelli
    Pages 179-226
  7. Ernesto Salinelli, Franco Tomarelli
    Pages 227-255
  8. Ernesto Salinelli, Franco Tomarelli
    Pages 257-283
  9. Ernesto Salinelli, Franco Tomarelli
    Pages 285-341
  10. Back Matter
    Pages 343-394

About this book


This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations. The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty; in the last chapter the detailed solution is given for most of them.


Markov chains difference equations discrete dynamical systems positive systems stability and bifurcations

Authors and affiliations

  • Ernesto Salinelli
    • 1
  • Franco Tomarelli
    • 2
  1. 1.Dipartimento di Studi per l’Economia e l’ImpresaUniversità del Piemonte OrientaleNovaraItaly
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02291-8
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02290-1
  • Online ISBN 978-3-319-02291-8
  • Series Print ISSN 2038-5714
  • About this book