Stoichiometric algal growth models are nonsmooth due to the Liebig's Law of Minimum and can generate new dynamics such as bistability for producer-grazer interactions. Environmental noises can be extremely important and change dynamical behaviors of a stoichiometric algal growth model. This talk involves two of our recent works on this respect. The first one is about the phenomena of noise-induced state switching between two stochastic attractors in a stochastically forced producer-grazer model. Namely, there is a frequent random hopping of phase trajectories between attracting basins of the attractors. The second is about the threshold dynamics in a stochastic algal growth model with the explicit incorporation of season-dependent light and nutrient availability. We also explore the effective way to inhibit algal blooms. The obtained results indicate that compared with removing algae periodically, blocking nutrient input from rivers constantly seems to be a more effective way to inhibit algal blooms with or without considering the environmental fluctuations, and the minimum blocking rate for successful inhibition of the stochastic system should be larger than the deterministic one.

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