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Dynamical systems in population biology. (English) Zbl 1023.37047
CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. 16. New York, NY: Springer. xiii, 276 p. (2003).
The declared aim of the author is to provide an introduction to the theory of periodic semiflows on metric spaces and its applications to population dynamics. He develops dynamical system approaches to various evolutionary models involving difference, functional, ordinary and partial differential equations, with special attention given to periodic and almost periodic phenomena.
In the first three chapters the underlying abstract mathematical concepts are introduced, comprising abstract discrete dynamical systems on metric spaces, global dynamics in certain types of monotone discrete dynamical systems on ordered Banach spaces, and periodic semiflows and Poincaré maps.
The results are then applied to continuous-time periodic population models, as in $$N$$-species competition in a periodic chemostat, almost periodic competitive systems, 3-species parabolic systems, a delayed predator-prey model, and travelling waves in a periodic reactor-diffusion model.
This is a book, written for the specialist.

##### MSC:
 37N25 Dynamical systems in biology 92D25 Population dynamics (general) 92-02 Research exposition (monographs, survey articles) pertaining to biology 37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory 39A11 Stability of difference equations (MSC2000) 37C55 Periodic and quasi-periodic flows and diffeomorphisms 34C25 Periodic solutions to ordinary differential equations 34K60 Qualitative investigation and simulation of models involving functional-differential equations 35K57 Reaction-diffusion equations 35R10 Partial functional-differential equations