Nonlinear analysis of narwhal dive records (data and animation)

Visualization of nonlinear analysis of narwhal-dive records Video 1: DepthNarwhal_raw_CWT_2minstep_LowRes.mp4 Legend: Animation of original depth readings and corresponding continuous wavelet transforms, CWTs, versus time-delay embedding reconstruction (m = 3, \(\tau\) = 375 s). Upper-left panel shows the raw data, where the largest red circle indicates the current time step, x(ti) (with the associated rate of depth change, in m/s), and two smaller red circles the corresponding x(ti + \(\tau\)) and x(ti + 2\(\tau\)). The tail with decreasing thickness in black corresponds to the final 20 min of data. Lower-left panel shows continuous wavelet transform (CWT) of the data with magnitude by color. The corresponding space–state reconstruction is presented to the right, where the lower-right panel is enlarged for a better display of the “core”. The tail of the preceding 20 min of data is shown in black to aid visual tracking of recent history. The red transparent background is the full embedding result. Video is 3,609 times faster than reality; frame time-step is 2 min. Video 2: attractor_6h_steps.mp4 Legend: State-space reconstruction animated using 6 h time-steps for highlighting long-term variability of narwhal diving behavior. Raw Data file: Whale3965nodry.csv Narwhal depth readings in m, at 1 sample per second (2013).

独角鲸潜水记录非线性分析可视化
视频1：DepthNarwhal_raw_CWT_2minstep_LowRes.mp4
图例：本动画展示原始深度读数、对应连续小波变换（continuous wavelet transform, CWT）与时间延迟嵌入重构（m=3，τ=375秒）的对比关系。左上方面板展示原始数据，其中最大的红色圆圈代表当前时间步x(ti)（附带深度变化速率，单位：m/s），两个较小的红色圆圈分别对应x(ti+τ)与x(ti+2τ)。黑色且厚度递减的尾部对应最后20分钟的数据集。左下方面板展示数据的连续小波变换（CWT）结果，颜色映射代表幅值大小。右侧为对应的状态空间重构结果，其中右下面板为放大视图，以便更清晰地展示“核心区域”。前20分钟数据的黑色尾部用于辅助视觉追踪近期历史轨迹，红色透明背景为完整的嵌入重构结果。本视频播放速度为现实的3609倍，帧时间步长为2分钟。

视频2：attractor_6h_steps.mp4
图例：本动画采用6小时间步长进行状态空间重构，用于凸显独角鲸潜水行为的长期变异性。
原始数据文件：Whale3965nodry.csv
独角鲸深度读数（单位：米），采样频率为1样本/秒，采集于2013年。