close to threshold. If noise is present, it will occasionally kick the system beyond $A'$ resulting in noise-induced oscillations ([*spiking*]{}).

Stochastic synchronization of instantaneously coupled neurons
=============================================================

We shall first consider two coupled FitzHugh-Nagumo systems as in eq. (\[eq:system\]) albeit without delay in the coupling ($\tau=0$). Noise can induce oscillations even though the fixed point is stable [@HAU06; @HOE07]. The noise sources then play the role of stimulating the excitable subsystems. Even if only one subsystem is driven by noise, it induces oscillations of the whole system through the coupling. In the following, we consider two nonidentical neurons, described by different timescales $\epsilon_1=0.005$, $\epsilon_2=0.1$, and set the noise intensity $D_2$ in the second subsystem equal to a small value, $D_2=0.09$, in order to model some background noise level. Depending on the coupling strength $C$ and the noise intensity $D_1$ in the first subsystem, the two neurons show cooperative dynamics.

![\[fig1\](a): Noise-induced oscillations in a single FitzHugh-Nagumo system ($C=0$) for a noise intensity $D_1=0.6$. The red dashed and dash-dotted lines denote the null-isoclines. Panel (b): Time series of two instantaneously coupled FitzHugh-Nagumo systems for different noise intensities $D_1$. The green (light grey), red (dark grey), and black curves correspond to $x_1$, 