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Predator–Prey Models

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

Abstract

A predator is an organism that eats another organism. A prey is an organism that a predator eats. In ecology, a predation is a biological interaction where a predator feeds on a prey. Predation occurs in a wide variety of scenarios, for instance in wild life interactions (lions hunting zebras, foxes hunting rabbits), in herbivore–plant interactions (cows grazing), and in parasite–host interactions.

Keywords

Equilibrium Point Truncation Error Global Variable Prey Population Logistic Growth 
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.

Supplementary material

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References

  1. 1.
    Coddington, E.A.: An Introduction to Ordinary Differential Equations. Dover, New York (1989)zbMATHGoogle Scholar
  2. 2.
    Butcher, J.C.: Numerical Methods for Ordinary Differential Equation. Wiley, New York (2008)CrossRefzbMATHGoogle Scholar
  3. 3.
    Strang, G.: Linear Algebra and Its Applications, 4th edn. Brooks/Cole, Belmont (2005)zbMATHGoogle Scholar
  4. 4.
    Gantmacher, F.R.: The Theory of Matrices, vol. 2. Chelsea, New York (1959)zbMATHGoogle Scholar
  5. 5.
    van den Driessche, P., Watmough, J.: Further notes on the basic reproduction number. In: Mathematical Epidemiology, pp. 159–178. Springer, Berlin/Heidelberg (2008)Google Scholar
  6. 6.
    Hale, J.K., Kocak, H.: Dynamics and Bifurcations. Springer, New York (1991)CrossRefzbMATHGoogle Scholar
  7. 7.
    Friedman, A., Hao, W., Hu, B.: A free boundary problem for steady small plaques in the artery and their stability. J. Diff. Eqs. 259, 1227–1255 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Louzoun, Y., Xue, C., Lesinski, G.B., Friedman, A.: A mathematical model for pancreatic cancer growth and treatment. J. Theor. Biol. 351, 74–82 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Friedman, A., Tian, J.P., Fulci, G., Chiocca, E.A., Wang, J.: Glioma virotherapy: the effects of innate immune suppression and increased viral replication capacity. Cancer Res. 66, 2314–2319 (2006)CrossRefGoogle Scholar
  10. 10.
    Day, J., Friedman, A., Schlesinger, L.S.: Modeling the immune rheostat of macrophages in the lung in response to infection. Proc. Natl. Acad. Sci. USA 106, 11246–11251 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Ohio State UniversityColumbusUSA

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