Discrete Dynamical Systems

  • Glenn Ledder
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


This short chapter presents the mathematics of matrix population models. The first section examines discrete linear systems using scalar notation and computer simulations. The simulations lead to the discovery of an asymptotic growth rate and stage structure, which we can determine by ad hoc methods for systems of only two or three components. The second section presents the matrix algebra that is needed as background for a more mathematical study of discrete linear systems. The two threads are united in the final section, which develops the ideas of eigenvalues and eigenvectors, methods for finding them, and interpretations for population models. The problem sets include population viability case studies for endangered falcons, cheetahs, and loggerhead turtles as well as population models for aphids and the teasel plant.


Matrix Model Population Model Dormant Seed Matrix Algebra Nonzero Solution 
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Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Glenn Ledder
    • 1
  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

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