Discrete Dynamical Models

Front Cover
Springer, Jun 11, 2014 - Mathematics - 394 pages
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.
 

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Contents

1 Recursive phenomena and difference equations
1
2 Linear difference equations
25
onestep scalar equations
84
bifurcations and chaos
125
onestep vector equations
179
6 Markovchains
227
7 Positive matrices and graphs
256
8 Solutions of the exercises
285
Appendix C Basic probability
351
Appendix D Linear Algebra
352
Appendix E Topology
363
Appendix F Fractal dimension
365
Appendix G Tables of Ztransforms
371
Appendix H Algorithms and hints for numerical experiments
375
References
381
Index
383

Appendix A Sums and series
342
Appendix B Complex numbers
347

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About the author (2014)

Prof. Franco Tomarelli, Dip. Matematica F. Brioschi, Politecnico di Milano, Italy Prof. Ernesto Salinelli, Dip. Di Studi per l'Economia e l'Impresa, UniversitÓ degli Studi del Piemonte Orientale A.Avogabro, Novara, Italy.