标题： 吸引域在无限维延迟系统中的组织结构：一种随机吸引域熵方法 显示英文标题

标题： Basin of attraction organization in infinite-dimensional delayed systems: a stochastic basin entropy approach

摘要： 麦基-格拉斯系统是一个延迟模型的典型例子，由于其多稳态特性，涉及许多周期性和混沌吸引子的共存，因此其动力学特别复杂。 在这些系统中，长期动力学的预测尤其具有挑战性，因为其维度是无限的，初始条件必须作为有限时间区间内的函数来指定。 在本文中，我们将最近提出的盆地熵扩展到随机采样任意高维空间。 通过将这种随机方法与初始条件空间中吸引子的盆地分数相结合，我们可以理解吸引盆地的结构及其相互混合的方式。 这里报告的结果使我们能够量化可预测性，从而了解轨迹的长期演化如何随初始条件而变化。 所使用的工具在研究无限维复杂系统方面可能非常有用。 显示英文摘要

摘要： The Mackey-Glass system is a paradigmatic example of a delayed model whose dynamics is particularly complex due to, among other factors, its multistability involving the coexistence of many periodic and chaotic attractors. The prediction of the long-term dynamics is especially challenging in these systems, where the dimensionality is infinite and initial conditions must be specified as a function in a finite time interval. In this paper we extend the recently proposed basin entropy to randomly sample arbitrarily high-dimensional spaces. By complementing this stochastic approach with the basin fraction of the attractors in the initial conditions space we can understand the structure of the basins of attraction and how they are intermixed. The results reported here allow us to quantify the predictability giving us an idea about the long-term evolution of trajectories as a function of the initial conditions. The tools employed can result very useful in the study of complex systems of infinite dimension.