Extinction in Systems of Interacting Biological Populations
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).
KeywordsSaddle Point Full System Divergence Theorem Heteroclinic Orbit Major Outbreak
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