结构连通祖母动力系统吸引子的可分性
On the Separability of Attractors in Grandmother Dynamic Systems with Structured Connectivity
摘要：
复杂网络和动态系统研究的结合将在未来几十年产生一些最有趣的理论和应用科学成果。目前的工作解决了一个特别重要的相关方面，即量化如何以及分离的吸引子可以在动态系统强调四种类型的复杂网络（Erdens-Rényi，Barabási-Albert，Watts-Strogatz和地理模型）。注意力集中在祖母动态系统，其中每个状态变量（与每个节点相关联）用于表示特定的原型模式（吸引子）。通过假设吸引子通过扩散过程在其相邻节点之间传播其影响，可以忽略特定动态的特定细节，并将注意力集中在这些吸引子之间的可分性上。这个属性是定义在两个分离指数（一个单独的每个原型和其他考虑直接的邻居）反映的平衡和接近吸引子的激活后的网络扩散过程。分离指数也考虑到邻里被认为是更多的信息，而最好的可分性观察到的Watts-Strogatz和地理模型。通过相关分析和通径分析研究了各参数对分离度的影响。所得到的结果表明，一些测量的拓扑结构和动力学之间的关系的潜在的特殊重要性。
英文摘要：
The combination of complex networks and dynamic systems research is poised to yield some of the most interesting theoretic and applied scientific results along the forthcoming decades. The present work addresses a particularly important related aspect, namely the quantification of how well separated can the attractors be in dynamic systems underlined by four types of complex networks (Erdős-Rényi, Barabási-Albert, Watts-Strogatz and as well as a geographic model). Attention is focused on grandmother dynamic systems, where each state variable (associated to each node) is used to represent a specific prototype pattern (attractor). By assuming that the attractors spread their influence among its neighboring nodes through a diffusive process, it is possible to overlook the specific details of specific dynamics and focus attention on the separability among such attractors. This property is defined in terms of two separation indices (one individual to each prototype and the other considering also the immediate neighborhood) reflecting the balance and proximity to attractors revealed by the activation of the network after a diffusive process. The separation index considering also the neighborhood was found to be much more informative, while the best separability was observed for the Watts-Strogatz and the geographic models. The effects of the involved parameters on the separability were investigated by correlation and path analyses. The obtained results suggest the special importance of some measurements in underlying the relationship between topology and dynamics.
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