Abstract. Lake eutrophication ecosystems tend to exhibit bistable kinetics with two preferential configurations of oligotrophic and eutrophic states, and perturbations in the environmental parameters can cause regime shifts between two alternative stable states, yielding catastrophic regime shifts. In this article, we study stochastic kinetics of regime shifts in a time-delayed lake eutrophication ecological system, where the environmental parameters are assumed to be disturbed by both input and loss external noises. The dynamical behavior of stochastic delay on the regime shifts between oligotrophic and eutrophic states is analyzed using numerical simulations. Time delays in loss and recycling processes are considered. It is shown from time series and probability distribution that noises and delays can induce regime shifts between two stable states. Theoretical analyses are used to support our numerical simulations. By using the mean first passage time (MFPT) technique, we also discuss the escape time problem between two stable states in time-delayed ecosystems. A detailed study of the MFPT depending on various noise characteristics is performed, and the main results are compared for different cases of time delays.

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Intracellular calcium oscillation with time delay and correlated noises was investigated in this paper by means of stochastic simulation. The time evolution and stationary probability distribution (SPD) of Ca 2+ concentration in the cytosol and in an IP 3 -insensitive pool were calculated. The results indicate that: (i) the intracellular calcium oscillation is suppressed with increasing the delay time τ but is enhanced with increasing the external noise intensity D; (ii) the structure of the SPD exhibits a transition from a single peak to double peaks and the biggest peak shrinks as the external noise intensity D increases; (iii) the structure of the SPD exhibits a transition from double peaks to a single peak and the biggest peak grows as the delay time τ increases.

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