Population dynamics: general results from local analysis
Population dynamics: general results from local analysis
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人口动态：当地分析的一般结果
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Thilo Gross
中科院分区：
文献类型：
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作者：
Thilo Gross
在这篇论文中，提出了一种新的方法来制定和分析一般模型。在一般模型中，状态变量之间的相互作用并不局限于特定的函数形式。相反，它们由一般函数描述。这种方法用于制定和研究一般食物链和食物网的模型。这项工作表明，一般模型可以分析的局部分歧理论的框架。为了有效地计算分支，导出了一种数学方法--结式法。结果法和通用建模方法的应用揭示了著名的富集悖论的新的通用解决方案。此外，对一般模型的研究也证明了三个以上营养级的系统一般都存在混沌参数区域。对生态食物网的研究表明，有一大类食物网在性质上与食物链相似。最后，它表明，强形式的著名的竞争排斥原则只发生，因为某些退化，存在于简单的生态模型。
In this thesis a new approach to the formulation and analysis of general models is presented. In general models the interaction between state variables is not restricted to specific functional forms. Instead they are described by general functions. This approach is used to formulate and study models of general food chains and food webs. This work illustrates that general models can be analysed in the framework of local bifurcation theory. In order to compute bifurcations efficiently a mathematical technique, the method of resultants, is derived. Application of the method of resultants and the general modelling approach reveals a new, general solution to the famous paradox of enrichment. Furthermore, the investigation of general models prove that chaotic parameter regions generally exist in systems with more than three trophic levels. The investigation of ecological food webs shows that a large class of food webs behaves qualitatively similar to food chains. Finally, it is shown that the strong form of the famous competitive-exclusion principle only occurs because of certain degeneracies that exist in simple ecological models.