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arXiv 0906.0381q-bio.PE
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某些食物网的局部动力学等价性

Local dynamical equivalence of certain food webs

Thilo Gross, Ulrike Feudel

摘要:

理论生态学的一个重要挑战是找到复杂食物网的良好的粗粒度表示。在这里,我们使用的方法,广义建模表明,它可能会制定一个粗粒度的算法,保存的局部动态模型。我们展示了具有不同数量物种的食物网的例子,这些物种具有完全相同的局部分叉图。基于这些观察,我们制定了一个猜想,其中复杂的食物网的人口可以分组到一个单一的变量,而不改变当地的动态。作为一个例子,我们使用这个猜想表明,混沌区域一般存在于一类食物网的参数空间中的三个以上的营养级。虽然我们的猜想是目前只适用于相对特殊的情况下,我们相信,它的适用性可以大大扩展,如果一个更复杂的参数映射中使用的模型减少。

英文摘要:

An important challenge in theoretical ecology is to find good, coarse-grained representations of complex food webs. Here we use the approach of generalized modeling to show that it may be possible to formulate a coarse-graining algorithm that conserves the local dynamics of the model exactly. We show examples of food webs with a different number of species that have exactly identical local bifurcation diagrams. Based on these observations, we formulate a conjecture governing which populations of complex food webs can be grouped together into a single variable without changing the local dynamics. As an illustration we use this conjecture to show that chaotic regions generically exist in the parameter space of a class of food webs with more than three trophic levels. While our conjecture is at present only applicable to relatively special cases we believe that its applicability could be greatly extended if a more sophisticated mapping of parameters were used in the model reduction.

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