• To apply the theory of planar systems to modeling interacting species. On completion of this chapter the reader should be able to

  • plot solution curves to modeling problems for planar systems;

  • interpret the results in terms of species behavior.


Phase Portrait Stable Manifold Mutual Exclusion Solution Curve Grey Squirrel 
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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Recommended Reading

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    F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.CrossRefMATHGoogle Scholar
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    Y. Lenbury, S. Rattanamongkonkul, N. Tumraysin, and S. Amornsamankul, Predator-prey interaction coupled by parasitic infection: Limit cycles and chaotic behavior, Math. Comput. Model., 30-9/10 (1999), 131–146.Google Scholar
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    R. E. Kooij and A. Zegeling, Qualitative properties of two-dimensional predator-prey systems, NonlinearAnal. Theory Meth. Appl., 29 (1997), 693–715.MathSciNetCrossRefMATHGoogle Scholar
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    E. C. Pielou, Mathematical Ecology, Wiley, New York, 1977.Google Scholar
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    V. Volterra, Variazioni e fluttuazioni del numero d’individui in specie animali conviventi, Mem. R. Accad. Naz. Lincei, 2-3 (1926), 30–113.Google Scholar
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    A. J. Lotka, Elements of Physical Biology, William and Wilkins, Baltimore, 1925.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Stephen Lynch
    • 1
  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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