发表机构
University of Bath; Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB)（巴斯大学; 跨学科物理与复杂系统研究所 IFISC (CSIC-UIB)）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构建无序耦合的逻辑斯蒂映射系统，发现即使最小无序也会消除倍周期级联并引发高维混沌，而强均匀耦合可恢复级联，揭示了动力系统现象对无序的脆弱性及新现象的出现。
AI 中文摘要
逻辑斯蒂映射是低维混沌研究中的典型模型。另一方面，高维混沌则出现在具有许多相互作用和异质耦合组分的无序系统中。在此，我们构建了一个由许多通过无序耦合相互作用的逻辑斯蒂映射组成的系统。结合动态平均场理论、随机矩阵理论和数值模拟，我们表明即使是最小量的无序也能消除传统逻辑斯蒂映射中的倍周期级联。相反，我们发现了一个向高维混沌的转变，其特征是一种此前未在无序系统中报道过的振荡不稳定性。我们还表明，当映射之间存在足够强的均匀耦合时，传统倍周期级联的要素得以恢复。我们的发现表明，动力系统中众所周知的现象在面对无序时可能是脆弱的。与此同时，新的现象出现了，这些现象既不见于简单的低维动力学，也不见于高维无序系统。
英文摘要
The logistic map is a quintessential model in the study of low-dimensional chaos. High-dimensional chaos, on the other hand, presents itself in disordered systems with many interacting and heterogeneously coupled components. Here, we formulate a system of many logistic maps, interacting through disordered couplings. Using a combination of dynamic mean-field theory, random matrix theory and numerical simulations, we show that even the smallest amount of disorder can remove the period-doubling cascade in the conventional logistic map. Instead we find a transition to high-dimensional chaos, marked by an oscillatory instability not previously reported for disordered systems. We also show that with sufficiently strong homogeneous coupling between the maps one recovers elements of the conventional period-doubling cascade. Our findings indicate that well-known phenomena in dynamical systems can be fragile in the face of disorder. At the same time, new phenomena emerge that are neither found in simple low-dimensional dynamics nor in high-dimensional disordered systems.
Comments41 pages, 17 figures
