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The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Ornstein–Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.

A single-mode laser noise model driven by quadratic colored pump noise and biased amplitude modulation signal is proposed. The analytic expression of signal-to-noise ratio is calculated by using a new linearized procedure. It is found that there are three different typies of stochastic resonance in the model: the conventional form of stochastic resonance, the stochastic resonance in the broad sense, and the bona fide SR.

By adding frequency modulated signals to the intensity equation of gain–noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.

According to a linear equation of the laser intensity of single-mode laser with input signal, we compute the generalized signal-to-noise ratio (GSNR) in the instantaneous-state of the single-mode laser, which is driven by two colored noises and correlated in the form of an e-exponential function. We detect that the stochastic resonance (SR) also occurs on instantaneous state at any time. Furthermore we discuss the GSNR trend to stable state in three different forms when taking different signal frequencies.

By adding frequency modulated signal to the equation of the laser intensity of the gain-noise model of the single-mode lasers, we use the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity, which is driven by two white noises correlated in the form of δ function. The result shows that the SNR shows typical stochastic resonance with the change of intensities of the pump noise and quantum noise. As the amplitude of a modulated signal has an effect on the SNR， it shows suppression, monotonic increase, resonance, suppression and resonance and so on， with the varing of the frequencies of the carrier signal and modulated signal.

By adding modulation wave to the equation of the laser intensity in the gain-noise model of the single-mode laser, we use the linear approximation method to calculate the power spectrum and signal-to-noise ratio(SNR) of the laser intensity, which is driven by two color noises correlated in the form of exponential function. The result shows that the correlated time and the correlated strength between the noises have great effect on the stochastic resonance(SR), and the variations of SNR with the frequency of the carrier signal ω and the modulator signal Ω are quite different from the curve of variation of white noise.

By adding modulated wave to the equation of the laser intensity of the gain-noise model of the single-mode lasers, we use the linear approximation method to calculate the power spectrum and signal-to-noise ratio(SNR) of the laser intensity, which is driven by two white noises correlated in the form of δ function. The result show that the SNR shows stochastic resonance with the varing of not only intensities of the pump noise and quantum noise，but also the frequency of a high frequency carrier signal and frequency of a low frequency periodical signal.

We have detected the stochastic resonance(SR) phenomenon by studying the output signal-to-noise ratio (SNR) of the linear model of single-mode laser, which is driven by two color noises correlated in the form of an exponential function. Moreover, we also discuss the influence on SNR from the noise (noise intens ity, correlated strength and correlation time between noises) and signal (signal frequency and signal amplitude).