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Discrete Dynamical Models (UNITEXT, nr. 76)

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en Limba Engleză Carte Paperback – 17 Dec 2013
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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Specificații

ISBN-13: 9783319022901
ISBN-10: 3319022903
Pagini: 412
Dimensiuni: 155 x 235 x 20 mm
Greutate: 6.20 kg
Ediția: 2014
Editura: Springer
Colecția Springer
Seriile UNITEXT , La Matematica per il 3+2

Locul publicării: Cham, Switzerland

Public țintă

Upper undergraduate

Cuprins

​1 Recursive phenomena and difference equations.- 2 Linear difference equations.- 3 Discrete dynamical systems: one-step scalar equations.- 4 Complex behavior of nonlinear dynamical systems: bifurcations and chaos.- 5 Discrete dynamical systems: vector equations.- 6 Markov chains.- 7 Matrix.- 8 Solutions.

Recenzii

From the book reviews:
“The text, intended for undergraduate students, is translated from its Italian third edition … . The book is made of seven chapters, plus one devoted to solutions to proposed exercises, and eight complements. … All chapters include a number of exercises (184 in total).” (Giuseppe Gaeta, zbMATH, Vol. 1301, 2015)

Notă biografică

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

Caracteristici

​The multi-disciplinary and modellistic approach provides a broad overview of the applications
A large number of step-by-step exercises and their worked solutions help the reader to learn quickly
The notion of chaotic dynamics is introduced through an in-depth study of the logistic model
Vector-valued discrete dynamical systems are focussed especially in connection to Markov chains, positive systems, demography and page-rank algorithm