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(t_i) (with the associated rate of depth change, in m/s), and two smaller red circles the corresponding x(t_i + \(\tau\)) and x(t_i + 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).