Figure 4. Theory of weakly coupled oscillators (TWCO).

(A) Schematic illustration of the model. Two limit-cycle oscillators (here symbolized by metronomes) that mutually interact with strength ε and dependent on function G(θ). Each oscillator has its own intrinsic frequency ω and the difference is termed detuning Δω. Each oscillator additionally had phase noise η. (B) The single differential equation used for analysis. (C) Output example from numerical simulation of Equation 1. The phase precession is shown above and the ΔIF is shown below. Notice the ΔIF modulations over time. (D) ΔIF modulations averaged as a function of Δphase. (E–J) Equivalent behavior as in the examples shown in Figure 3. Top panels E-G show the modulation of the instantaneous frequency difference as a function of phase difference. Note that the instantaneous Δphase at which the ΔIF is minimal (yellow dot) is smaller when the interaction strength is larger (compare F, G to E). Bottom panels (H–J) show the phase difference probability distributions. Black bars are numerical simulation results, red lines indicate the analytical solutions. (E.H) Large detuning and low interaction strength. (F,I) Large detuning and strong interaction strength. (G,J) Small detuning and large interaction strength.