由I类不透明度生成的水平可见性图形
Horizontal Visibility graphs generated by type-I intermittency
摘要：
在水平可见度图理论中研究了I型通向（或脱离）混沌的不确定性路径。为了这个目的，我们解决了单峰映射产生的轨迹接近反正切分岔和构造，根据水平可见性算法，其相关的图形。我们展示了层流发作和混沌爆发的交替如何在所得到的图形结构中具有指纹。因此，我们推导出一个唯象理论，预测几个网络参数的定量值。特别是，我们预测，层流趋势大小的平均长度的特征幂律缩放完全继承在图形度分布的方差中，与数值吻合良好。我们还报告了数值证据的特征幂律缩放的李雅普诺夫指数作为一个函数的距离的切线分叉是继承在图中的块熵的度分布的类似缩放。此外，我们能够重铸的全套HV图产生的间歇动力学到一个重整化群框架，其图论RG流的不动点占不同类型的动态。我们还建立了这个流的非平凡不动点符合相切条件，相应的不变图表现出极大熵性质。
英文摘要：
The type-I intermittency route to (or out of) chaos is investigated within the Horizontal Visibility graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct, according to the Horizontal Visibility algorithm, their associated graphs. We show how the alternation of laminar episodes and chaotic bursts has a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values of several network parameters. In particular, we predict that the characteristic power law scaling of the mean length of laminar trend sizes is fully inherited in the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of the block entropy over the degree distribution. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization group framework, where the fixed points of its graph-theoretical RG flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibit extremal entropic properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
