Dynamical systems in population biology
Dynamical systems in population biology
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DOI：
10.1007/978-0-387-21761-1
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发表时间：
2003
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影响因子：
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通讯作者：
Xiao-Qiang Zhao
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文献类型：
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作者：
Xiao-Qiang Zhao
种群动力学是数学生物学中的一个重要课题。一个中心问题是研究建模系统的长期行为。这些系统中的大多数都由各种演化方程控制，如差分方程、常微分方程、泛函方程和偏微分方程（见[253，206，334，167，77]）。我们知道，互动群体通常生活在一个波动的环境中。例如，物理环境条件，如温度和湿度以及食物、水和其他资源的可用性通常随季节或每日变化而变化。因此，更现实的模型应该是非自治系统。特别地，如果模型中的数据是具有相称周期的时间的周期函数，则出现周期系统;如果这些周期函数具有不同的（最小）周期，则我们得到概周期系统。现有的工具书，从动力系统的角度来看，主要集中在自治生物系统。赫斯的书[152]是一个很好的参考周期抛物边值问题与人口动力学的应用。自本书出版以来，人们对周期、渐近周期、概周期甚至一般非自治生物系统进行了广泛的研究，这反过来又推动了动力系统理论的进一步发展。
Population dynamics is an important subject in mathematical biology. A central 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, eg,[253, 206, 334, 167, 77]). 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 [152] 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.