The Research On Stochastic Resonance Phenomena In Linear Systems Driven By Cross-correlated Noises

Over the last decades, amazing progress has been made in the study of stochastic dynamics, various stochastic dynamic systems appear in many natural scientific and social science fields. Stochastic resonance (SR) is one of the important research subjects among them. In this paper, using the analytic methods, we investigated stochastic resonance in a cross-correlated-noise driving linear system. Specifically, the main work of our paper consists of the following:(1) The statistical characteristics of white and colored noises are described, respectively, and the cross-correlated forms between different noises are presented. The conception,mechanism,basic theory and applied areas of SR are introduced in detail.(2) Using the statistical method of the output signal average, the SR phenomenon in an overdamped harmonic oscillator with time modulated cross-correlation between multiplicative and additive dichotomous noises is studied. In the presence of the time modulated cross correlation, the influence of the cross-correlated intensity on SR is analyzed. Results show that, for appropriate noise and signal intensity, as the cross-correlated intensity increases, the peak value of SR undergoes a nonmonotonic process.(3) Applying the ensemble averaging method, SR phenomenon in an underdamped harmonic oscillator driven by multiplicative and additive dichotomous noises is studied. In the present of time independent as well as the time modulated cross-correlation, the characteristics of the system output are analyzed. It is found that, due to the time modulated cross-correlation, the cross-correlated intensity enters into the expression of the system output. Adjusting the cross-correlated intensity, we obtained doubly stochastic resonance.(4) SR phenomenon in a biased periodic force driving overdamped linear system is investigated. In order to make our research more approach to the actual situation, we introduced more commonly cross-correlated O-U noises. It is found that, O-U noise can induce SR. Moreover, considering the time modulated cross-correlation between multiplicative and additive noises, we not only obtain the SR, but also obtain the suppression phenomenon.