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Extinction in Systems of Interacting Biological Populations

  • Johan Grasman
  • Onno A. van Herwaarden
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

In Sect. 4.3 we already dealt with a single population that has a stochastic logistic dynamics. In this chapter we fully analyse two examples of two-dimensional systems: a prey-predator system and the epidemiological problem of contact between infectives and susceptibles. The method we use is rather complex. It is for that reason that we do not expect that the method will be taken over by population biologists. In Sect. 7.3 we show how the problem of extinction of one population within a system of interacting populations can be approached in a more conceivable way using a stochastic logistic approximation. Other biological applications of stochastic exit are found in Capocelli and Ricciardi (1971), Ebeling and Engel-Herbert (1982), and Cobb and Zacks (1985).

Keywords

Saddle Point Full System Divergence Theorem Heteroclinic Orbit Major Outbreak 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Johan Grasman
    • 1
  • Onno A. van Herwaarden
    • 1
  1. 1.Department of MathematicsAgricultural UniversityWageningenThe Netherlands

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