Logical vibrational resonance in a symmetric bistable system: Numerical and experimental studies

Abstract

In previous studies, double harmonic signals as external driving forces have been used for inducing logical vibrational resonance to facilitate the control of logic operations. It requires the bias parameter to break the symmetry of the bistable system. In hardware circuits, symmetric bistable system circuits are easy to build and even using few components. To address the problem of maintaining the symmetry of the system while inducing the logical vibrational resonance, we take advantage of the property that an anharmonic signal with a constant component in the Fourier series can replace the bias parameter to induce logical vibrational resonance. We add an anharmonic low-frequency signal to the symmetric bistable system as a slowly-varying signal. In addition, we add another high-frequency signal as a fast-varying signal. Through numerical simulation, we find the optimal logic output region of the system and the logic output region is explained by using bifurcation theory. Then, noise is added to the system to demonstrate its effect on the optimal logic output region. Finally, the simulation results are further verified by a hardware circuit. Both simulation and experimental results prove the occurrence of logical vibrational resonance and its necessary condition in the symmetric bistable system.