Effect of the correlation between internal noise and external noise on logical stochastic resonance in bistable systems

Some noisy nonlinear systems could be exploited to operate reliable logic operation in an optimal window of noise intensity, which is termed as logical stochastic resonance (LSR). We investigated the LSR phenomenon in bistable systems when internal noise and external noise are correlated. The LSR effect is evaluated by the success probability of the obtained desired output with various combinations of logic inputs. It is shown that the or-nor, and-nand, and Latch operations still can operate reliably with the correlated internal noise and external noise. A positive correlation strength tends to enhance or-nor logic and suppress and-nand logic. The negative correlation strength tends to suppress or-nor logic and enhance and-nand logic. The results provide possible corroboration for implementing reliable LSR when internal noise and external noise are correlated.

Figure 1

For the or-nor logic operation, from top to bottom, panel (a) shows the stream of input $I=I_1+I_2$; panels (b–d) show the output of the system with different correlation $C=–0.9$, $C=0$, and $C=0.9$, respectively. The parameter values $D_M=0.25$, $D_A=0.3$, $b=0.5$ are used.

Figure 2

For the and-nand logic operation, from top to bottom, panel (a) shows the stream of input $I=I_1+I_2$; panels (b–d) show the output of the system with different correlation $C=–0.9$, $C=0$, and $C=0.9$, respectively. The parameter values $D_M=0.25$, $D_A=0.3$, $b=–0.5$ are used.

Figure 3

The success probability $P$ of the or-nor logic versus noise intensity $D_M$ are plotted with different correlation $C$. The bias $b$ is set to 0.475 ($C=–0.9$), 0.5($C=0$), 0.525($C=0.9$), respectively. The parameter value $D_A=0.1$ is used.

Figure 4

The success probability $P$ of the and-nand logic versus noise intensity $D_M$ are plotted with different correlation $C$. The bias $b$ is set to –0.525 ($C=–0.9$), –0.5 ($C=0$), $–0.475$ ($C=0.9$), respectively. The parameter value $D_A=0.1$ is used.

Figure 5

Points marking where the or-nor logic (red) and and-nand logic (blue) are obtained with probability 1 for different correlation strengths: (a) $C=–0.9$, (b) $C=0$, and (c) $C=0.9$. The parameter value $D_A=0.1$ is used.

Figure 6

Points marking where the latch operation (green) are obtained with probability 1 for different correlation strengths: (a) $C=–0.9$, (b) $C=0$, and (c) $C=0.9$.The parameter value $D_A=0.1$ is used.