Advertisement

Quadratic Two-Species Population Models

  • James C. Frauenthal
Part of the The Umap Expository Monograph Series book series (UMAP)

Abstract

We proceed now to look at a rather general model for the interaction of two biological species. Special cases of this model will represent Predator-Prey, Competitive and Mutualistic interactions. We will however be able to demonstrate a very general result for all such models. Specifically, we will show that the models almost never admit periodic (cyclic) solutions. This of course means that in terms of finding a model which describes an ecosystem which is known to behave in a cyclic manner, the model discussed below is not adequate.

Keywords

Equilibrium Point Hilbert Function Simple Closed Curve Cyclic Manner Unique Critical 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. The material in this section is drawn from two teaching modules by C.S. Coleman. At the present time, these are available from:Google Scholar
  2. Professor W.F. Lucas 334 Upson Hall Cornell University Ithaca, NY 14853Google Scholar
  3. Coleman, C.S., “Hilbert’s 16th Problem: How Many Cycles?”, MAA Workshop on Modules in Applied Mathematics, Cornell University, 1976.Google Scholar
  4. Coleman, S.C., “Quadratic Population Models: Almost Never Any Cycles”, MAA Workshop on Modules in Applied Mathe mathematics, Cornell University, 1976.Google Scholar

Copyright information

© Education Development Center, Inc. 1979

Authors and Affiliations

  • James C. Frauenthal
    • 1
  1. 1.Applied Mathematics and StatisticsState University of New YorkStony BrookUSA

Personalised recommendations