A stochastic mechanism causing long or short transients near a bifurcation point

When a bifurcation parameter in a deterministic model becomes a stochastic process, additional new stochastic processes may arise near a critical parameter value. By examining the sample paths of a population model with a strong Allee effect, in which the bifurcation parameter is defined as an Ornstein–Uhlenbeck (OU) process, we find that transient times before extinction may be extended or shortened according to the excursions of the OU process. We find the distributions of transient times as they depend on process parameters.