Fig. 22

Simulation of the stochastic Morris–Lecar model for subthreshold Na⁺ oscillations with \(N=10\) and \(\varepsilon = 0.01\). (Adapted from Ref. [21].) Other parameter values as in Fig. 21. (a) Plot of the approximate phase \(\theta_{t} - t\omega_{0}\) in green (with \(\theta_{t}\) satisfying equation (6.26) and the exact variational phase (satisfying (6.19)) \(\beta_{t} - t\omega_{0}\) in black. On the scale \([-\pi,\pi]\) the two phases are in strong agreement. However, zooming in, we can see that the phases slowly drift apart as noise accumulates. The diffusive nature of the drift in both phases can be clearly seen with the typical deviation of the phase from \(\omega_{0} t\) increasing in time. (b) Stochastic trajectory around limit cycle (dashed curve) in the \(v,w\)-plane. The stable attractor of the deterministic limit cycle is quite large, which is why the system can tolerate quite substantial stochastic perturbations