Second, The Value Of Stochastic Resonance, Noise-driven Linear System

In this paper, we consider stochastic linear system driven by dichotomous noise and a periodic signal. In chapter 1, the study significance of stochastic res-onance and its status are briefly introduced; in chapter 2, we have analytically described the study method of stochastic resonance; the contents of Chapters 3 and 4 are my research work:analytically investigated the effect of inertial mass on stochastic resonance with multiplicative dichotomous noise and a periodic signal driven in a linear system in the underdamped case, and the correlation effect of stochastic resonance in a linear system driven by correlated asymmetric dichotomous noises and periodic signal in the overdamped case, respectively.In dealing with this type of linear system theory, we usually use Shapiro-Loginov method. Finally we calculate the expressions of output signal ampli-tude and signal-to noise ratio(SNR). The results on numerical simulations a(?) shown:(1)The effect of inertial mass on a two-order linear system with dichoto-mous noise and a periodic signal is investigated in the underdamped case.And we find the inertial mass also influences the SNR of the system, and causes it to display many types of resonance phenomena:(â…°) at some fixed noise intensities, the output signal amplitude with inertial mass exhibits the structure of a single peak and single valley, or even two peaks if the dichotomous noise is asymmet-ric; (â…±) in the case of asymmetric dichotomous noise, the inertial mass can cause non-monotonic behaviour of the output signal amplitude with respect to noise intensity; (â…²) the curve of SNR versus inertial mass displays a maximum in the case of asymmetric dichotomous noise, i.e., a resonance-like phenomenon, while it decreases monotonically in the case of symmetric dichotomous noise; (iv) if the noise is symmetric, the inertial mass can induce stochastic resonance in the system.(2) we have analytically investigated Phenomenon of stochastic resonance in a linear system driven by correlated asymmetric dichotomous noises and periodic signal in the overdamped case.In the interval of existence on stable solutions,we find that the system could possess a intrinsic vibrational fre-quency, which cooperate with the periodic signal and Krammer rate to make the system exhibit some peculiar statistical properties:(â…°)At some fixed multi-plicative noise intensities, the output signal amplitude with frequency exhibit the structure of a weak peak, even no peak as the dichotomous noise is asym-metric; (â…±)In the case of asymmetric dichotomous noise, the signal frequency can cause non-monotonous behavior of the output signal amplitude with re-spect to multiplicative noise intensity; (â…²)The curve of SNR with frequency has a weak peak and a trough in the case of symmetric dichotomous noise, but no peak with asymmetric; (â…³)Whether the multiplicative noise is symmet-ric or asymmetric, the noise can enhance response of the system; (â…´)The SNR increases with the correlation strength between the two noises decreasing.