Abstract
In this paper, an asymmetric bistable potential system driven by a high-frequency periodic source with weak aperiodic input is studied. Then steady-state response of the system is decomposed into fast motion and slow motion, and the analytical approximation solution of the system is obtained. Based on this, we find out the sufficient conditions for the noise-free logical stochastic resonance (NFLSR). Next, we illustrate two essential features of NFLSR, namely the sign invariant and the initial value independent features to obtain the sufficient conditions for the occurrence of the NFLSR phenomenon. Then, the sufficient conditions are verified by numerical simulation, and the results show that the sufficient conditions and numerical simulation are consistent. Finally, the success probability of the logic gate is defined and analysis of this success probability is made, indicating that properly adjusting the parameters of system can control the occurrence of NFLSR and thus receive an expected logic gate, which has not been considered in the symmetric situation. The results of this study can be applied to obtain the expected logic gate or even establish a certain logic system we expect.
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