Dynamical systems in population biology / Xiao-Qiang Zhao

Auteur: Zhao, Xiao-Qiang (1963-) - AuteurType de document: Livre numériqueCollection: CMS books in mathematics ; 16Langue: anglaisÉditeur: New York : Springer, cop. 2003 ISBN: 9780387003085 Note: 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. (zbMath) Sujets MSC: 37N25 Dynamical systems and ergodic theory -- Applications -- Dynamical systems in biology
92D25 Biology and other natural sciences -- Genetics and population dynamics -- Population dynamics (general)
37C55 Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Periodic and quasiperiodic flows and diffeomorphisms
34C25 Ordinary differential equations -- Qualitative theory -- Periodic solutions
34K60 Ordinary differential equations -- Functional-differential and differential-difference equations -- Qualitative investigation and simulation of models
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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. (zbMath)

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