Identification of a Group’s Physiological Synchronization with Earth’s Magnetic Field

Figures

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  Figure 1. An example of the local magnetic field intensity data (measured in Lithuania during the time period between 2015/02/26 01:00:01 and 2015/02/26 03:00:01).

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  Figure 2. An example of the spectrogram for the magnetic field data presented in Figure 1. Frequency resolution is 14096, Δθ=4 h, Δω=52 Hz, ω∈[0;52]Hz.

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  Figure 3. Time series X=(X1,…,Xn) representing a numerical solution to Equation (4) with initial conditions x(0)=0; x′(0)=0.8.

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  Figure 4. Examples of attractors for different time lag values. In (a) τ=4; (b) τ=12; (c) τ=23; (d) τ=31; (e) τ=43; (f) τ=50.

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  Figure 5. Shifting the origin to the center of mass of the attractor for τ=4: (a) the original attractor; (b) the origin shifted to the center of the mass of the attractor.

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  Figure 6. Sliced diagrams of the attractors shown in Figure 4.

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  Figure 7. The identification of optimal time lag value τ*.

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  Figure 8. Time series X (a) and Y (b) and the difference X−Y (c), obtained from numerical integration of the coupled nonlinear pendulum model (Equation (5)). Dotted lines separate time intervals with different values for the coupling parameters.

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  Figure 9. The sets of optimal time lags (a) τ*j(X) and (b) τ*j(Y) for the time series depicted in Figure 8. Circles in (c) denote the absolute differences τ*j(X,Y) between optimal time lags for X and Y. The solid red line in (c) corresponds to the averaged absolute differences A(X,Y)=[τ¯1(X,Y)τ¯2(X,Y) … τ¯16(X,Y)].

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  Figure 10. The scheme of the application of Algorithm C on the experimental data. The horizontal axis of the depicted data corresponds to the indices of the time series.

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  Figure 11. Dendrogram plot for the two-day (2015/02/27 18:05:00 through 2015/03/01 18:05:00) data. Numbers on the X axis represent participants (numbered from 1 to 20).

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  Figure 12. The variation of the slow dynamics of the geometrical synchronization constructed from optimal time lags for participant 7 (red line) and participant 20 (blue line) for the time period between 2015/02/27 18:05:00–2015/03/01 18:05:00.