An Asymmetric Bistable System The Mean First Passage Time And Stochastic Resonance Study

The mean first-passage time (MFPT) is introduced to depict the transient properties of the systems and stochastic resonance (SR) is a very important phenomenon in stochastic dynamics. They have attracted considerable attention on the research of theory and the potential applications. In this thesis, we investigate the mean first-passage time and the phenomenon of stochastic resonance of the asymmetric bistable system by the widely used information theory method. The main work is as following:1. According to the steepest-descent approximation, we get the MFPT's expression of asymmetric bistable system driven by correlated noises; the effect of parameters on the MFPTs is discussed. It is found that the effect of multiplicative noise on the MFPTs along two opposite directions is distinct. The resonance appears on the curve of the MFPT from left potential to right one when the multiplicative noise intensity is increased; the opposite one is monotonously changing with the increase multiplicative noise intensity. The effect of the strength of correlation noises on the MFPT is different if the value of the correlation noises strength is in diverse range.2. The mean first-passage time of asymmetric bistable system driven by color correlated noises is investigated, based on the theory of adiabatic limit. Numerical result shows that: with the increasing of the strength of correlations between noises, suppression appears on the curve of the MFPT at first, and then there is a peak on the curve. On the effect of the correlation time between the noises, the curves of MFPT appear resonance with small value of the bias of the system; if we choose the big value of the bias of the system, the curves of MFPT is monotonously decrease as the correlation time between the noises increases.3. The phenomenon of SR in an asymmetric bistable system driven by multiplicative colored noise and additive white noise and a periodic rectangular signal are studied. The periodic modulated signal is replaced by the periodic rectangular signal,...