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A one-dimensional overdamped system consisting of a symmetric periodic potential, a constant bias force and a trichotomous noise was investigated. In the frame of master equations, we derived analytical expression of its current. By means of numerical calculations, the results indicate that the current first increases, then decreases and finally increases with the bias force increasing, i.e., an absolute negative mobility (ANM) phenomenon. Our further investigations presented dependence of the ANM phenomenon on parameters of the noise. Its intrinsic physical mechanism was also open up, and a minimal model with ANM phenomenon is demonstrated.

The simplified incidence function model with cross-correlated noises was employed to study the stability of a metapopulation perturbed by environments. Through numerically computing the stationary probability distribution function (PDF) and stochastically simulating the extinction time of a metapopulation, we found that: (i) The multiplicative noise intensity D inhibits the fluctuation of dynamic variable while the additive noise intensity α intensifies it, whether there is a correlation between the multiplicative noise and the additive noise; (ii) As the correlation strength (λ) between them is greater than zero, there is an optimal D in which the PDF curve deviates furthest from the extinction position, and another optimal D which maximally delays the extinction time of a metapopulation; (iii) For the constant D and α, the increment of λ not only upgrades the probability that patches are occupied by a metapopulation, but also delays the time that a metapopulation goes to extinction.