A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data
Fig 4
Estimated coupling function of electronic circuit.
(a) The diagram shows the coupling direction between oscillators of the same frequency. The first oscillator was coupled to the second oscillator. (b) The red line shows the estimated phase coupling function with the natural frequency in the same-frequency coupling case. The dashed black line shows the theoretical coupling function. The coupling function from the second to first oscillator Γ12 is identically zero. When there is no interaction, the coupling function is nearly zero. The gray dots show the experimental data points. (c) The coupling functions from the first to second oscillator Γ21. (d) The blue line shows the phase difference histogram of the experimental data in the case of 1:1 phase locking (experimental histogram). The red line shows the simulated histogram calculated in the phase oscillator model estimated from the experimental data (estimated histogram). The dashed black line shows the simulated histogram calculated in the phase oscillator model using the theoretical natural frequencies and coupling functions (theoretical histogram). (e) In the cross-frequency coupling case, the slow oscillator was coupled to the fast oscillator. (f) The coupling function from the fast to slow oscillator is identically zero. (g) The coupling function from the slow to fast oscillator. (h) The experimental, estimated, and theoretical histogram in the 1:2 phase-locking case.