When the nonlinearity of a system matches with its input signal and its input noise, the additivity of the noise would not decrease the system output signal-to-noise ratio (SNR on the contrary, it can greatly improve the SNR of the system, i.e., there exists an optimum input noise intensity which enables the SNR reaches its maximum value. The above phenomenon is called stochastic resonance (SR). The SR in a broad sense means the non-monotonic behavior of the output signal (output signal-to-noise ratio, mean output value, etc) as a function of some characteristics of the noise (noise intensity or noise correlation time) or of some characteristics of the system and input signal (amplitude or frequency).SR is different from traditional linear methods (such as correlation, filter etc.) in signal detection, it can turn parts of noise energy into signal energy to increase the system SNR .In this dissertation, the SR phenomena of some linear and nonlinear models are investigated. The method of weak signal detection based on the SR phenomenon of some models is proposed.The main research production and innovation of this dissertation are listed as follows:1. The SR in a bias first-order linear system subject to multiplicative and additive dichotomous-noise (DN) is investigated. It is shown that the SNR is a non-monotonic function of the correlation time of the multiplicative and additive DN, and it varies non-monotonously with the intensity of the multiplicative DN as well as with the frequency and the bias of the stimulation signal. Moreover, the SNR decreases as the increase of the system bias and the intensity of the additive DN, while the SNR increases as the increase of the intensity of the cross noise between the multiplicative and additive DN.2. The SR phenomenon of an RLC series circuit perturbed by white Gaussian noise is investigated. It is shown that the output-amplitude-gain (OAG) is a non-monotonic function of the noise strength and the external stimulation frequency. By choosing appropriate parameters of the noise and the system, the OAG of the noisy system can be larger than that of the noise-free system. This result is of some theoretical significance, i.e., one can use this property to improve the detection of weak signal by the perturbation of the system parameter.3. An over-damped nonlinear Duffing oscillator driven by a periodic force and a Gaussian white noise is studied. Using the equivalent linearization method, we find the phenomenon of conventional SR and bona fide SR takes place on the curve of the OAG when the OAG is plotted as a function of the noise strength as well as the frequency of the stimulation signal.4. The SR in a mono-stable system subject to multiplicative and additive noise is investigated. It is shown that the SNR is a non-monotonic function of the system bias, the system parameters as well as the intensities of the multiplicative and additive noise. An adaptive weak signal detection approach based on the SR of the mono-stable system is proposed.5. Taking the fault diagnose of a switch mode power and the data enhancement of a noisy PCM data as detecting objects, the application of SR of the mono-stable system in weak signal detection is studied.