二维时滞混沌映射的树和模的自组织
Self-organization in Trees and Motifs of Two-Dimensional Chaotic Maps with Time Delay
摘要：
研究了无标度树和树形子图（4-星）的边耦合的二维混沌标准映射，节点间具有非辛耦合和时滞。除了混沌和规则的2-周期运动外，耦合映象系统在很宽的耦合强度范围内还表现出多种动力学效应。这包括动力学局部化，涌现的周期性，和奇怪的非混沌吸引子的外观。在奇异吸引子附近，我们发现在返回时间到相空间的指定部分的间隔中存在长程相关。我们证实了有限时间李雅普诺夫稳定性的分析。我们也给出了一些定量的证据，如何在4星图案的小尺度动力学参与的集体行为在整个网络的起源。
英文摘要：
We study two-dimensional chaotic standard maps coupled along the edges of scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling and time delay between the nodes. Apart from the chaotic and regular 2-periodic motion, the coupled map system exhibits variety of dynamical effects in a wide range of coupling strengths. This includes dynamical localization, emergent periodicity, and appearance of strange non-chaotic attractors. Near the strange attractors we find long-range correlations in the intervals of return-times to specified parts of the phase space. We substantiate the analysis with the finite-time Lyapunov stability. We also give some quantitative evidence of how the small-scale dynamics at 4-star motifs participates in the genesis of the collective behavior at the whole network.
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