Effect of spatially correlated noise on coherence resonance in a network of excitable cells

We study the effect of spatially correlated noise on coherence resonance (CR) in a Watts-Strogatz small-world network of Fitz Hugh–Nagumo neurons, where the noise correlation decays exponentially with distance between neurons. It is found that CR is considerably improved just by a small fraction of long-range connections for an intermediate coupling strength. For other coupling strengths, an abrupt change in CR occurs following the drastic fracture of the clustered structures in the network. Our study shows that spatially correlated noise plays a significant role in the phenomenon of CR reinforcing the role of the clustered structure of the system.

Figure 1

The coherence factor $S$ versus noise intensity $D$ for several values of coupling strength on (a) regular network $(p=0)$ and (b) completely random network $(p=1)$ with spatial correlation length of noise $\lambda =0$. (c), (d) are the same curves for $p=0$ and $p=1$ with $\lambda =2$, respectively. Average number of neighbors $k=6$. Number of elements $N=101$. Coupling strength $g$ varies from $g={10}^{-2.5}$ to $g={10}^{-0.5}$ with 0.25 step of exponent. Base curves represent $g={10}^{-2.5}$. As coupling strength increases, the peak of $S$ shifts to a stronger noise.

Figure 2

The maximal coherence factor $S_m$ as a function of network randomness $p$ for different values of $\lambda$, when coupling strength is (a) very weak $g={10}^{-2.5}$, (b) rather weak $g={10}^{-2.25}$, (c) optimal $g={10}^{-1.75}$, (d) rather strong $g={10}^{-1.25}$, and (e) very strong $g={10}^{-0.75}$. $\lambda$ is varied from $\lambda =0$ (local noise) to $\lambda =6$ with a step 2. $S_m$ curve goes down with increasing $\lambda$ except in (a).

Figure 3

Clustering coefficient $C$ (open circle) and characteristic path length $L$ (solid circle) as a function of $p$ for Watts-Strogatz small-world networks with $N=101$ and $k=6$. They are normalized by each value at $p=0$.

Figure 4

Optimal noise intensity $D_{\mathit{pot}}$ as a function of $p$ for various $\lambda$ including 0 (diamond), 2 (circle), 4 (triangle), and 6 (rectangle). (a) $g={10}^{-1.25}$ and (b) $g={10}^{-0.75}$.