Fig. 4.

Relation between entrainment performance and phase sensitivity and free-energy dissipation. a The minimum number of cycles needed for entrainment t_e/τ versus the PRC amplitude for different choices of (γ₁, γ₂). The energy dissipation per period ΔW is shown by the color of the data points. The log-log plot in the inset clearly shows t_e/τ scales inversely with the PRC amplitude. b t_e/τ decreases with ΔW. The inset shows t_e/τ (represented by the color) in the $\left(-log{\gamma }_1,-log{\gamma }_2\right)$ space. c Autocorrelation function C_xx(t) versus time t. The amplitude first decays exponentially and then reaches a constant $e^{-D{t}_{\mathrm{e}}}$ in agreement with Eq. (10). The phase dynamics in the cases without ($\epsilon$ = 0) and with ($\epsilon$ > 0) external driving signal are illustrated in the inset. d The phase diffusion constant D, inferred from phase variance, decreases with the energy dissipation ΔW. The external driving signal strength $\epsilon$ = 0.1 for all simulations