中文摘要：

目前已有的随机共振理论对于随机共振系统的非线性动力学行为及其发生机理阐释得不够具体和明晰,本文从分析一阶非线性Duffing方程的动力学特性入手,推导得到非自治Duffing方程的吸引子曲线,基于该曲线和输入信号之间的映射关系分析了系统输出的动力学行为,并由此进一步定性分析了随机共振现象发生的动力学机理;研究表明：作用于系统的内禀信号能推动系统动点沿吸引子曲线移动,它对系统的输出起内在的和本质的作用,而噪声在一定条件下能够诱发系统产生跃迁行为;文章最后利用该动力学机理对已有的调参数和调阻尼等基于随机共振的微弱信号检测方法作了统一和延拓.

英文摘要：

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.