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Discrete dynamics

  • Mimmo Iannelli
  • Andrea Pugliese
Chapter
  • 1.8k Downloads
Part of the UNITEXT book series (UNITEXT, volume 79)

Abstract

Difference equations, recursive relations, discrete mathematics,… namely rules for building number sequences, have been on the stage for centuries, mainly to define approximating procedures, especially in connection with numerical methods. However, in more recent years, iterative procedures arose in the context of the modeling of natural phenomena, and the concept of a (time) discrete dynamical system has been developed for a parallel and alternative approach to the theory based on differential equations. In  Chap. 3 we have in fact discussed several population models, embedded in the framework of a time discrete description, here we give an account of some basic fact and results that we have used in the analysis. Some of the basic references have been already quoted in  Chap. 3: 2 and 5; a more introductory presentation including Ordinary Differential Equations and Discrete Dynamical Systems is in 4 while 1 gives extended applications to ecological studies. Finally, 3 provides the basic results of the qualitative theory, while elementary and less elementary bifurcations are discussed in 6 and 7.

Keywords

Periodic Orbit Discrete System Discrete Dynamical System Floquet Multiplier Transcritical Bifurcation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    1. Caswell, H.: Matrix Population Models. Second edition, Sinauer Associates Inc. (2001)Google Scholar
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    2. Devaney, R.L.: A First Course in Chaotic Dynamical Systems. Westview Press (1992)zbMATHGoogle Scholar
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    3. Elaydi, S.: An Introduction to Difference Equations. Springer (2005)zbMATHGoogle Scholar
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    4. Hirsch, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems & an Introduction to Chaos. Second edition, Elsevier (2004)zbMATHGoogle Scholar
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    5. Holmgren, R.A.: A First Course in Discrete Dynamical Systems. Springer (1994)CrossRefzbMATHGoogle Scholar
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    6. Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer (2010)Google Scholar
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    7. Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer (1990)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mimmo Iannelli
    • 1
  • Andrea Pugliese
    • 1
  1. 1.Department of MathematicsUniversity of TrentoItaly

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