识别逻辑映射中动力学转变的结构
Identifying the structure of dynamical transitions in logistic map
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中文总结 AI 辅助
该研究以逻辑映射为对象，构建编码振幅跳变的复杂网络，利用全局与局部网络度量识别动力学转变的关键特征，揭示了轨道图中特殊抛物线形模式与分岔图周期点分布的关联。
中文摘要 AI 辅助
非线性动力学系统表现出由涨落驱动的丰富动力学状态与转变。为理解动力学转变过程中涨落的模式，本研究考察逻辑映射中从混沌到有序转变的结构特征。我们将涨落定义为振幅跳变，并将其编码为复杂网络，其中节点代表振幅水平，连边代表不同振幅区间之间的转变。我们发现，全局网络度量可识别倍周期分岔点、周期态与混沌态区域，包括内部危机事件。利用局部网络度量，我们还揭示了轨道图中新颖的特殊抛物线形模式，表明其与分岔图中稳定和不稳定周期点的分布具有相似性。
英文摘要
Nonlinear dynamical systems manifest rich variety of dynamical states and transitions driven by fluctuations. To understand the pattern of fluctuations during dynamical transitions, we investigate the structural features of chaos to order transition in logistic map. We determine fluctuations as amplitude jumps and encode them onto a complex network where nodes represent amplitude levels and links represent transitions between distinct amplitude bins. We discover that global network measures identify points of period doubling, regimes of periodicity and chaos, including interior crises events. Using local network measures, we also unravel novel peculiar parabolic-shaped patterns in the orbit diagram that we show are reminiscent of the distribution of stable and unstable periodic points in the bifurcation diagram.
