Figure 12

Numerical results for the range of validity of \(f_{SI}=f_{2}\). (a) As in Fig. 6, we plot the firing rate of the SI cell as a function of the input-2 frequency \(f_{2}\), but for a variety of other parameter values. The range of \(f_{2}\) for which Theorem 4.1 guarantees that \(f_{SI}=f_{2}\) is given by Eq. (15). For all three conditions shown in the figure (input-1 frequency 40 Hz, 45 Hz, and 40 Hz with a weaker FS→SI synapse—see Appendix D.1) we have \(m=2\). Under the first two conditions we have \(c\approx 0.016\) (estimated from simulations, see text), and in the third condition \(c\approx 0.01325\), thus the range that Eq. (15) predicts \(f_{SI}=f_{2}\) should hold is \(f_{2}\in [15.15,20)\) for the first condition, \(f_{2}\in [16.54,22.5)\) for the second, and \(f_{2}\in [15.81,20)\) for the third condition shown. The simulation results show that in each case \(f_{SI}=f_{2}\) indeed holds at least in the corresponding range, verifying the theoretical predictions. Dashed gray line: diagonal. (b) The SI firing rate as a function of input-1 frequency \(f_{1}\). The range of \(f_{1}\) for which \(f_{SI}=f_{2}\) is predicted to hold is given by Eq. (17), but the parameter m in general depends on \(f_{1}\). In all three conditions shown here (input-2 frequency 16.357 Hz, 18.357 Hz, and 16.357 Hz with a weaker FS→SI synapse—see Appendix D.1) the equality \(f_{SI}=f_{2}\) holds for a large range of input-1 frequencies