Daphnia revisited: local stability and bifurcation theory for physiologically structured population models explained by way of an example
Daphnia revisited: local stability and bifurcation theory for physiologically structured population models explained by way of an example
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DOI：
10.1007/s00285-009-0299-y
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发表时间：
2010-08-01
影响因子：
1.9
通讯作者：
de Roos, Andre M.
中科院分区：
文献类型：
--
作者：
Diekmann, Odo;Gyllenberg, Mats;de Roos, Andre M.
我们考虑一般大小结构化的消费者群体和非结构化的资源之间的相互作用。我们表明，稳定性和分岔现象可以理解的两个延迟方程（更新方程的消费人口出生率耦合到延迟微分方程的资源集中）的系统的解决方案。由于这种系统的许多结果是可用的（Diekmann等人，在SIAM J Math Anal 39：1023-1069，2007中），我们可以从特征方程的分析中得出关于动力学行为的严格结论。我们导出了一类相当一般的人口模型的特征方程，包括基于Kooijman-梅斯水蚤模型的研究（Kooijman和梅斯，Ecotox Env Saf 8：254-274，1984; de鲁什等人，J Math Biol 28：609-643，1990）和Gurney-Nisbet引入的模型（Theor Popul Biol 28：150-180，1985）和Jones等人（J Math Anal Appl 135：354-368，1988），并且接下来通过特殊情况的分析或数值研究获得各种生态学见解。
We consider the interaction between a general size-structured consumer population and an unstructured resource. We show that stability properties and bifurcation phenomena can be understood in terms of solutions of a system of two delay equations (a renewal equation for the consumer population birth rate coupled to a delay differential equation for the resource concentration). As many results for such systems are available (Diekmann et al. in SIAM J Math Anal 39:1023-1069, 2007), we can draw rigorous conclusions concerning dynamical behaviour from an analysis of a characteristic equation. We derive the characteristic equation for a fairly general class of population models, including those based on the Kooijman-Metz Daphnia model (Kooijman and Metz in Ecotox Env Saf 8:254-274, 1984; de Roos et al. in J Math Biol 28:609-643, 1990) and a model introduced by Gurney-Nisbet (Theor Popul Biol 28:150-180, 1985) and Jones et al. (J Math Anal Appl 135:354-368, 1988), and next obtain various ecological insights by analytical or numerical studies of special cases.