Dynamics of Single Populations

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


This chapter develops the mathematics of discrete and continuous models for a single dynamic quantity. Separate sections introduce each type of model via simple examples and simulations, and two additional sections present the principal graphical methods: cobweb analysis for discrete equations and phase line analysis for continuous equations. The final section uses the graphical methods as motivation for the development of the linearized stability method. The examples and problem sets feature case studies for a variety of biological settings, including fishery models, insect population models, resource management, and lake eutrophication.


Continuous Model Discrete Model Phase Line Holling Type Stable Fixed Point 
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  1. 1.
    Britton NF. Essential Mathematical Biology. Springer, Berlin and New York (2004)Google Scholar
  2. 2.
    Carpenter SR, D Ludwig, and WA Brock. Management of eutrophication for lakes subject to potentially reversible change. Ecological Applications, 9: 751–771 (1999)Google Scholar

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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