Pinning noise-induced stochastic resonance

This paper proposes the concept of pinning noise and then investigates the phenomenon of stochastic resonance of coupled complex systems driven by pinning noise, where the noise has an $\alpha$-stable distribution. Two kinds of pinning noise are taken into account: partial noise and switching noise. In particular, we establish a connection between switching noise and global noise when Gaussian noise is considered. It is shown that switching noise can not only achieve a stronger resonance effect, but it is also more robust to induce the resonance effect than partial noise.

Figure 1

Probability density function of noise having a stable distribution. (a) Varying $\alpha$ when $\beta =0,\gamma =1,\text{and}\delta =0$. (b) Varying $\gamma$ when $\alpha =1.5,\beta =0,\text{and}\delta =0$.

Figure 2

The spectral amplification factor $R$ of globally coupled bistable systems plotted as a function of $\alpha$, $\gamma$, and $p_e$, when switching noise is considered. (a) $R$ as a function of $\alpha$ and $p_e$ when $\beta =0,\gamma =5\sqrt{2},\delta =0$, and $W=100$. (b) $R$ as a function of $\gamma$ and $p_e$ when $\alpha =2,\beta =0,\delta =0$, and $W=100$.

Figure 3

Properties of SR of coupled bistable systems with partial noise and switching noise. (a) Comparison of SR of coupled bistable systems with partial noise and switching noise when $\alpha =2,\beta =0,\gamma ={10}^{1.2},\delta =0$, and $W=100$. (b) Comparison of SR of globally coupled bistable systems with global noise and switching noise when $\alpha =2,\beta =0,\gamma ={10}^{1.2},\delta =0,\check{\gamma }=\sqrt{p}*{10}^{1.2}$, and $W=100$.

Figure 4

Results of SR of coupled bistable systems with partial noise and switching noise under different scale $N$, when $\alpha =2,\beta =0,\gamma ={10}^{1.2},\delta =0$, and $W=100$.

Figure 5

Results of SR of coupled bistable systems with partial noise and switching noise under different simulation time $W$, when $\alpha =2,\beta =0,\gamma ={10}^{1.2},\delta =0$, and $N=200$.

Figure 6

The approximating theory for the spectral amplification factor $R$ when $\alpha =2,\beta =0,\gamma ={10}^{1.2},\delta =0$, $W=100$, and $N=200$. $\overline{R}$ is an approximation of $R$.