集合种群网络的稳定划分
Stabilized Partitioning of Metapopulations Networks
摘要：
集合种群网络是一个多斑块生境系统，种群在生境斑块中生活和相互作用，个体通过扩散连接从一个斑块扩散到另一个斑块。栖息地斑块之间扩散联系的丧失会影响系统的稳定性。在这项工作中，我们确定是否存在（S）集（S）的分散连接删除导致分区（S）的集合种群网络到动态稳定的子网络。我们的研究发现，存在一个下界阈值Fiedler值，保证网络动力学的动态稳定性。必要和充分的数学条件，找到分区，导致子网络与所需的阈值Fiedler值已被导出，并举例说明。虽然在生态学背景下提出和讨论，它可以指出，这样的分区问题存在于任何空间离散，但连接动力系统与反应扩散。非生态学的例子是配电网、细胞内反应途径网络和高密度纳米流体芯片实验室应用。
英文摘要：
A metapopulations network is a multi-patch habitat system, where populations live and interact in the habitat patches, and individuals disperse from one patch to the other via dispersal connections. The loss of dispersal connections among the habitat patches can impact the stability of the system. In this work, we determine if there exist(s) set(s) of dispersal connections removal of which causes partitioning(s) of the metapopulations network into dynamically stable sub-networks. Our study finds that there exists a lower bound threshold Fiedler value which guarantees the dynamical stability of the network dynamics. Necessary and sufficient mathematical conditions for finding partitions that result in sub-networks with the desired threshold Fiedler values have been derived and illustrated with examples. Although posed and discussed in the ecological context, it may be pointed out that such partitioning problems exist across any spatially discrete but connected dynamical systems with reaction-diffusion. Non-ecological examples are power distribution grids, intra-cellular reaction pathway networks and high density nano-fluidic lab-on-chip applications.
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