Nonlinear dynamics of stochastic resonance and its application in the method of weak signal detection

According to the exited stochastic resonance theory, we cannot obtain the dynamic behavior of a stochastic resonance (SR) system intuitively. In order to reveal the dynamic mechanism of SR, a kind of first-order Duffing equation attractor is analyzed at first, and then the property of nonlinear Duffing equation is studied, based on which the nonautonomous Duffing equation attractor curve is deduced. The output of SR system can be obtained by mapping the input signal on the attractor curve, and the dynamic mechanism of SR is explained by using the mapping method. Analysis of the result indicates that the intrinsic signal can push the system to move along the attractor curve, and the noise can evoke a transition response of the system under the given conditions. Some exited SR weak signal detection methods, such as the parameter-adjustment and damping-adjustment are extended by the proposed dynamic mechanism.