The Modeling Study On The Environment-driven Growth Mechanism Of Phytoplankton

In this paper,dynamical models are developed to explore the mechanism of the phytoplankton growth driven by the environment.The main topics are as follows.Environmental stochasticity is ubiquitous in the natural environment,how-ever,the effect of environmental stochasticity on phytoplankton growth is still not clear.A stochastic nutrient-phytoplankton system is proposed to explore this effect.A stochastic ecological reproductive index is formulated to characterize the global dynamics.Numerical simulations are presented to investigate the long-time effect of water temperature,light,nutrients,and environmental noise on the dy-namic evolution of phytoplankton.It is shown that environmental stochasticity plays a negative role in the growth of phytoplankton.Through methods of hy-pothesis testing and interval estimation,the range of the phytoplankton density under the conditions of different environmental noise,temperature,light intensity,and nutrients is predicted.The rule of the spatial evolution of phytoplankton in its habitat is also a hot topic in the study of its growth mechanism.Based on the assumption of spatial heterogeneity,a reaction-diffusion system for phytoplankton growth is formulated.Theories of parabolic and elliptic equation analyze the dynamical properties of the system,and establish sufficient conditions for Turing instability.Numerical simulations explore the rule of the temporal and spatial evolution of phytoplankton under the conditions of different temperature,light intensity and nutrients.It is shown that the system presents a rich spatial distribution form when the diffusion rate of phytoplankton is lower than the diffusion rate of nutrients.The above-mentioned studies have assumed that temperature and light in-tensity are constant,and it is difficult to characterize the fact that phytoplankton blooms occur seasonally in the natural environment.In order to explore the mechanism of seasonal phytoplankton blooms,we develop a nonautonomous stoi-chiometric algal growth model incorporating a season-driven light intensity.The existence and stability of the positive periodic solution of the system are inves-tigated by the coincidence degree theory and the Liapunov method.Numerical simulations explore the effect of seasonal periodicity and nutrient content on the growth of phytoplankton.Studies show that the density of phytoplankton changes periodically with time.At the same time,due to the consideration of the effect of chemical element quota on phytoplankton growth,too high nutrient content can also limit the growth of phytoplankton.Because the model dynamics fit the data well,the model has strong feasibility.The model provides a certain theoretical basis for the control measures of seasonal phytoplankton blooms.