Effect of colored noise on logical stochastic resonance in bistable dynamics

Recently, Murali [Phys. Rev. Lett. 102, 104101 (2009)] showed that some noisy nonlinear dynamics could be exploited to design nonlinear logic gate based on stochastic resonance (SR). In the paper, inspired by the Murali's articles, we consider the logical stochastic resonance (LSR) phenomenon in a bistable system by cycling various combinations of two logic inputs, in the presence of exponentially correlated noise. The effect of the colored noise on the LSR is evaluated by the success probability of obtained desired logic output. The two major results are presented. First, it shows that the LSR effect can be obtained by changing noise intensity. The logic output is obtained most reliably at an intermediate noise band. There is still a plateau on performance curve of the success probability versus noise intensity. As correlation time increases, the optimal noise band shifts to higher level and peak performance is degraded from 100% accuracy. Due to the influence of the colored noise, the plateau is a bit low and not completely flat. On the other hand, the performance measure can evolve nonmonotonically as correlation time increases, and a SR-like effect is obtained as a result of correlation time. It shows that actually some finite correlation time is better than delta correlation time at certain noise intensities. The study might provide an example where LSR phenomenon can exist robustly in the presence of colored noise.