Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.
Zhao
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Weitere Infos & Material
* Introduction * Discrete Dynamical Systems * Monotone Dynamics * Nonautonomous Semiflows * A Discrete-time Chemostat Model * N-species Competition in a Periodic Chemostat * Almost Periodic Competitive Systems * Competitor-Competitor-Mutualist Systems * A Periodically Pulsed Bioreactor Model * A Nonlocal and Delayed Predator-Prey Model * Traveling Waves in Bistable Nonlinearities * Bibliography * Index
Dr. Xiao-Qiang Zhao is a professor in applied mathematics at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 40 papers and his research has played an important role in the development of the theory of periodic and almost periodic semiflows and their applications.
