Stochastic resonance in periodic potential driven by dichotomous noise

Periodic potential system is widely used in a lot of areas such as biological ratchet model of motor, Josephson junction in the field of physics, engineering mechanics of the damping pendulum model, etc. Meanwhile, in the study of stochastic resonance, noise is crucial for dynamical system evolution. There are mostly colored Gaussian noises with nonzero correlation times in practical problems. Dichotomous noises belong to the color noises, and they have some simple statistical properties. In this paper, we study the motion of a Brownian particle in a periodic potential, driven by both a periodic signal and a dichotomous noise. The periodic potential system is different from the bistable system, so we use multiple indexes to explain the stochastic resonance. We calculate the average input energy of the system and the average output signal amplitude and phase difference by using stochastic energetics. Then we discuss the influences of the dichotomous noise intensity, noise correlation time and asymmetric coefficient of potential energy on the stochastic resonance. The results show that with the increase of the noise correlation time, a minimum value and a maximum value occur on the curve of the average input energy, meanwhile, the phenomenon of resonance appears in the system. With the increase of the noise intensity, the value of noise correlation time becomes greater when the phenomenon of stochastic resonance appears. Therefore, the region of stochastic resonance becomes bigger as the noise intensity or the asymmetry coefficient increases. Moreover, with the increase of the noise intensity, a mono peak is found for the signal-to-noise ratio (SNR) of the system and the stochastic resonance appears in this system. With the increase of the noise intensity, we compare the change of the SNR, the average input energy, and the average output signal amplitude. We find that the values of the amplitudes of the average output signal and SNR are basically the same, while the values of the amplitude of the average input energy of the system are a little different. This is because during the process of periodic signal doing work to the system, noise does work and passive dissipation energy of the system occures. In addition, when the curves of the amplitude of the average output signal and SNR reach their corresponding minimum values, the phase difference between the output signal and input signal is minimal.