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Effects of time delay on the active rate of a bistable system was investigated. Using the steepest-descent approximation method, the analytical expression of the mean first passage time and the active rate of the bistable system with time delay was derived under the condition of small delay time. The numerical computations show that the time delay enhances the resonance suppression in the system.

The Levins model subjected to the noise is employed to study the stability of a metapopulation. The analytic expressions of the stationary probability distribution function and the mean extinction time of the metapopulation are obtained according to the Fokker-Planck Equation. The results show that for the case of no correlation between the additive noise and the multiplicative noise (=0, is the intensity of correlation between multiplicative and additive noise), the increase of the additive noise intensity weakens the stability of a metapopulation; for the case of 0, enhances the stability of a metapopulation. For -(c-e-D)2/(4cD)1, can induce the resonance restrain phenomenon. Meantime, there exists a critical value of D. When D is lower than the critical value, the stability of the system is enhanced.

The transient properties (e.g., the mean first passage time T) of the gene transcriptional regulatory system driven by colored cross-correlated noise are investigated. The approximate Fokker-Planck equation is obtained based on the Novikov theorem and the Fox approach and the explicit expression of the mean first passage time is derived. The numerical computation results show that for the case of strong correlation intensity and short correlation time，a successive switch process (i.e.，“on”→“off”→“on”) occurs; for tha case of weak correlation intensity and long correlation time，only one switch process occurs (i.e.，“on”→“off”). The reentrance phenomena appear in the gene transcriptional regulatory system.

The dynamical characters of a theoretical anti-tumor model under immune surveillance subjected to a pure multiplicative noise are investigated. The effects of pure multiplicative noise on the stationary probability distribution (SPD) and the mean first passage time (MFPT) are analysed based on the approximate Fokker-Planck equation of the system in detail. For the anti-tumor model, with the multiplicative noise intensity D increasing, the tumor population move towards to extinction and the extinction rate can be enhanced. Numerical simulations are carried out to check the approximate theoretical results. Reasonably good agreement is obtained.