Dynamics of a nutrient-phytoplankton model with random phytoplankton mortality. (7th March 2020) - Song, Da; Fan, Meng; Yan, Shihan; Liu, Meng
Highlights: Analytical and numerical results are obtained for a stochastic nutrient-phytoplankton model. Stochastic ecological reproductive index is proposed to depict the threshold dynamics. Effect of water temperature, light, nutrient, and environmental noise is explored. The theory of Markov semigroup is applied to prove the existence and stability of invariant density. Statistical methods are applied to get some estimations in numerical simulations. Abstract: This study formulates a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution, stochastic boundedness, and stochastically asymptotic stability are well explored. A stochastic ecological reproductive index R 0 s is formulated to characterize the global dynamics. The theoretical analysis demonstrates that, if R 0 s < 1, then phytoplankton dies out with probability one; if R 0 s > 1 and some other conditions hold, then there exists an invariant and asymptotically stable density of the system and the approach involves integral Markov semigroups theory. Numerical simulations are presented to illustrate the analytical findings and to investigate the long-time effect of water temperature, light, nutrients, and environmental noise on the dynamic evolution of phytoplankton.