  Considerable evidence suggests that anticipating sudden shifts from one state
to another in bistable dynamical systems is a challenging task, examples
include ecosystems, financial markets, complex diseases, etc. In this paper, we
investigate the effects of additive, multiplicative and cross correlated
stochastic perturbations on determining regime shifts in a bistable gene
regulatory sys- tem, which gives rise to two distinct states of low and high
concentrations of protein. We obtain the stationary probability density and
mean first passage time of the system. We show that increasing
additive(multiplicative) noise intensity induces regime shift from a low(high)
to a high(low) pro- tein concentration state. However, an increase in cross
correlation intensity always induces regime shifts from high to low protein
concentration state. For both bifurcation (often called tipping point) and
noise induced (called stochastic switching) regime shifts, we further explore
the robustness of recently developed critical slowing down based early warning
signal (EWS) indicators (e.g., rising variance and lag-1 autocorrelation) on
our simulated time series data. We identify that using EWS indicators,
prediction of an impending bifurcation induced regime shift is relatively
easier than that of a noise induced regime shift in the considered system.
Moreover, the success of EWS indicators also strongly depends upon the nature
of noise. Our results establish the key fact that finding more robust indicator
to forewarn regime shifts for a broader class complex natural systems is still
in its infancy and demands extensive research.
