Stochastic resonance subject to multiplicative and additive noise: The influence of potential asymmetries

The influence of potential asymmetries on stochastic resonance (SR) subject to both multiplicative and additive noise is studied by using two-state theory, where three types of asymmetries are introduced in double-well potential by varying the depth, the width, and both the depth and the width of the left well alone. The characteristics of SR in the asymmetric cases are different from symmetric ones, where asymmetry has a strong influence on output signal-to-noise ratio (SNR) and optimal noise intensity. Even optimal noise intensity is also associated with the steepness of the potential-barrier wall, which is generally ignored. Moreover, the largest SNR in asymmetric SR is found to be relatively larger than the symmetric one, which also closely depends on noise intensity ratio. In addition, a moderate cross-correlation intensity between two noises is good for improving the output SNR. More interestingly, a double SR phenomenon is observed in certain cases for two correlated noises, whereas it disappears for two independent noises. The above clues are helpful in achieving weak signal detection under heavy background noise.

Figure 1

SNR for well-depth asymmetry subject to two independent noises as a function of (a) both multiplicative noise intensity $D$ and asymmetric ratio $\alpha$, where $A=0.02$ and $\epsilon =0.01$; (b) both additive noise intensity $\epsilon$ and $\alpha$, where $D=0.01$ and $A=0.02$; (c) both periodic force amplitude $A$ and $\alpha$, where $D=2$ and $\epsilon =0.01$; (d) $D$, where $A=0.02$ and $\epsilon =0.01$; (e) $\epsilon$, where $D=0.01$ and $A=0.02$; and (f) $\alpha$, where $A=0.02$ and $\epsilon =0.01$. Note that the color of the curves in the inset is consistent with that in figure (f).

Figure 2

SNR for well-width asymmetry subject to two independent noises as a function of (a) both multiplicative noise intensity $D$ and asymmetric ratio $\alpha$, (b) both additive noise intensity $\epsilon$ and $\alpha$, (c) both periodic force amplitude $A$ and $\alpha$, (d) $D$, (e) $\epsilon$, and (f) $\alpha$. Note that other parameters are the same as in Fig. 1 and the color of the curves in the inset is consistent with that in figure (f).

Figure 3

SNR for both well-depth and well-width asymmetry subject to two independent noises as a function of (a) both multiplicative noise intensity $D$ and asymmetric ratio $\alpha$, (b) both additive noise intensity $\epsilon$ and $\alpha$, (c) $D$, and (d) $\epsilon$. Note that other parameters are the same as in Fig. 1.

Figure 4

SNR for well-depth asymmetry subject to two correlated noises as a function of (a) cross-correlation intensity $\lambda$, where $\epsilon =0.01$ and $D=1.2$; (b) multiplicative noise intensity $D$, where $\epsilon =0.01$ and $\alpha =0.5$; (c) additive noise intensity $\epsilon$, where $D=0.1$ and $\alpha =0.5$; and (d) asymmetric ratio $\alpha$, where $\lambda =0.6$ and $\epsilon =0.01$. Note that the amplitude of periodic force always remains as $A=0.02$.

Figure 5

SNR for well-width asymmetry subject to two correlated noises as a function of (a) cross-correlation intensity $\lambda$, (b) multiplicative noise intensity $D$, (c) additive noise intensity $\epsilon$, and (d) asymmetric ratio $\alpha$. Note that other parameters are the same as in Fig. 4.

Figure 6

SNR for both well-depth and well-width asymmetry subject to two correlated noises as a function of (a) cross-correlation intensity $\lambda$, (b) multiplicative noise intensity $D$, (c) additive noise intensity $\epsilon$, and (d) asymmetric ratio $\alpha$. Note that other parameters are the same as in Fig. 4.

Figure 7

SNR when cross-correlation intensity $\lambda =1$: for well-depth asymmetry as a function of (a) multiplicative noise intensity $D$, where $\epsilon =0.02$, and (b) additive noise intensity $\epsilon$, where $D=0.02$; for well-width asymmetry as a function of (c) multiplicative noise intensity $D$, where $\epsilon =0.02$, and (d) additive noise intensity $\epsilon$, where $D=0.1$. Note that the amplitude of periodic force always remains as $A=0.02$.

Figure 8

SNR when cross-correlation intensity $\lambda =-1$: for well-depth asymmetry as a function of (a) multiplicative noise intensity $D$, where $\epsilon =0.02$, and (b) additive noise intensity $\epsilon$, where $D=0.2$; for well-width asymmetry as a function of (c) multiplicative noise intensity $D$, where $\epsilon =0.2$, and (d) additive noise intensity $\epsilon$, where $D=0.2$. Note that the amplitude of periodic force always remains as $A=0.02$ and the color of the curves in the inset is consistent with that in figure (a).