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Permanence and the dynamics of biological systems. (English) Zbl 0783.92002
From the authors’ abstract: A basic question in mathematical biology concerns the long-term survival of each component, which might typically be a population in an ecological context, of a system of interacting components. Many criteria have been used to define the notion of long- term survival. We consider here the subject of permanence, i.e., the study of the long-term survival of each species in a set of populations. These situations may often be modeled successfully by dynamical systems and have led to the development of some interesting mathematical techniques and results. Our intention here is to describe these and to consider their applications to several of the most frequently used models occurring in mathematical biology.
We particularly wish to include and cover those models leading to problems that are essentially infinite-dimensional, for example reaction- diffusion equations, and to make the discussion accessible to a wide audience, we include a chapter outlining the fundamental theory of these topics.

MSC:
92B05 General biology and biomathematics
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