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Dynamics of First Order Difference Equations

  • Saber N. Elaydi
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Difference equations usually describe the evolution of certain phenomena over the course of time. For example, if a certain population has discrete generations, the size of the n + 1st generation x(n + 1) is a function of the nth generation x(n).

Keywords

Equilibrium Point Difference Equation Asymptotic Stability Bifurcation Diagram Periodic Point 
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.

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References

  1. [1]
    E. C. Pielou, An Introduction to Mathematical Ecology, Wiley Interscience, New York, 1969.zbMATHGoogle Scholar
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    M. Feigenbaum, “Quantitative Universality for a Class of Nonlinear Transformations,” J. Stat. Phys. 19 (1978), 25–52.MathSciNetzbMATHCrossRefGoogle Scholar
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    T.Y. Li and J.A. Yorke, “Period Three Implies Chaos,” Am. Math. Monthly 82 (1975), 985–992.MathSciNetzbMATHCrossRefGoogle Scholar

Bibliography

  1. R. Devaney, A First Course in Chaotic Dynamical Systems: Theory and Experiments, Addison-Wesley, Reading, 1992.zbMATHGoogle Scholar
  2. D. Gulick, Encounters with Chaos, McGraw-Hill, New York, 1992.Google Scholar
  3. R. Mickens, Difference Equations, Van Nostrand Reinhold, New York, 1990.zbMATHGoogle Scholar
  4. J.T. Sandefur, Discrete Dynamical Systems, Clarendon, Oxford, 1990.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Saber N. Elaydi
    • 1
  1. 1.Department of MathematicsTrinity UniversitySan AntonioUSA

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