Stochastic resonance in higher-order networks driven by colored noise

Abstract

We investigate stochastic resonance (SR) in an ensemble of coupled overdamped bistable oscillators driven by colored noise. The networks incorporate the weighted contributions of both pairwise coupling and 2-simplex coupling. Our findings show that these higher-order interactions further exacerbate the suppression effect of colored noise on SR, reducing the peak of resonance curves and shifting the optimal noise intensity toward higher values. To clarify the underlying mechanism, we establish a close connection between SR and the four-stage variation in network synchronization level. Specially, the synchronization extremes explain the effect of higher-order coupling and colored noise on SR. Our analysis reveals that higher-order interactions do not reverse, but primarily promote the spatial propagation of suppression effects due to colored noise.

Figures (8)

• Figure 1: Mean-field time series $X(t)$ on the higher-order network (1) for different noise intensities $D$. Parameters: $A=0.2$, $\Omega=0.1$, $N=50$, $\alpha=1$, $\sigma=0.1$. From top to bottom, $D=0.06,\,0.16,\,0.60$. (a) White noise (white-noise limit $\tau=0$); (b) Colored noise ($\tau=0.5$). The red curves in panels (a2) and (b2) show the external periodic forcing $A\sin(\Omega t)$.
• Figure 2: Spectral amplification factor $S$ versus noise intensity $D$ for different correlation time $\tau$ on the higher-order network (1), $\alpha=1$. (a) Representative curves for $\tau=0,\,0.1,\,0.2$. (b) Heat map of $S$ in the parameter plane $(D,\tau)$. Other parameters: $A=0.2$, $\Omega=0.1$, $N=50$, $\sigma=0.1$.
• Figure 3: Spectral amplification factor $S$ versus noise intensity $D$ for different weight $\alpha$ of higher-order interactions in the network (1). (a) Purely pairwise network ($\alpha=0$); (b) $\alpha=0.25$; (c) $\alpha=0.5$; (d) $\alpha=0.75$. For the white-noise case with the largest peak (best resonance) in each panel, the corresponding peak values indicated by red dashed lines are $S_{\mathrm{peak}}=15$, $14.2$, $13.5$, and $12.7$, respectively.
• Figure 4: Spectral amplification factor $S$ versus noise intensity $D$ for different coupling strengths $\sigma$ on the higher-order network ($\alpha=1$). Four values of the coupling strength are shown: $\sigma=0.05,\,0.1,\,0.2,\,0.4$. The solid and dotted lines indicate the results of $\tau=0.1$ and $\tau=0.2$, respectively.
• Figure 5: Effect of the correlation time $\tau$ on the spectral amplification factor in higher-order networks driven by power-limited colored noise. (a) $S$ versus $D^{\mathrm{pl}}$ for $\tau=0,\,0.1,\,0.2$; (b) $D^{\mathrm{pl}}_{\mathrm{optimal}}$ and $S_{\mathrm{peak}}$ versus $\tau$. Other parameters are the same as in Fig. \ref{['fig:fig2']}.