Figure 4.

Finite-sample effects amplify the oscillations of Q. The two panels show the overlay of the three envelopes Ω (light gray region with solid line), $\overline{\Omega }$ (medium gray region with dashed line), and Ω_u (dark gray region with solid line) together with two trajectories of Q(t) obtained by solving numerically (by using the Euler-Maruyama method with time step Δt = 10⁻³) the Langevin model (red line) and the deterministic system of Eq. 2 (blue line) with the same, random initial condition. The two panels show two independent realizations of the models with different stochastic, initial conditions. The plots provide an example of two possible scenarios in which the intrinsic stochasticity of the Langevin model amplifies the oscillations of the deterministic system (a) or it triggers the emergence of new oscillations (b). To see this figure in color, go online.