标题： 从多重分形时间序列中出现的无标度网络 显示英文标题

标题： Scale-free networks emerging from multifractal time series

摘要： 连接动力系统和图论的方法在过去几年中引起了越来越多的兴趣，其应用范围从对不同种类动力学的详细比较到对实证数据的表征。 在这里，我们研究了时间信号的（多）分形特性对适当投影网络拓扑的影响，这种特性常见于来自混沌或奇异吸引子的序列中。 依靠盒子计数形式化方法，我们将盒子映射到网络的节点，并建立解析表达式，将盒子的自然测度与其在图表示中的度相连接。 我们确定了导致无标度拓扑出现的条件，并通过广泛的数值模拟验证了我们的发现。 显示英文摘要

摘要： Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data. Here we investigate the effects of the (multi)fractal properties of a time signal, common in sequences arising from chaotic or strange attractors, on the topology of a suitably projected network. Relying on the box counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology, and validate our findings with extensive numerical simulations.