Study On The Stochastic Dynamics Model Of Marine Plankton Growth

Taking into account the process of growth and reproduction of plankton in the ocean is inevitably affected by uncertain factors,based on three different control mechanisms,in this thesis,we establish several types of random phytoplankton growth models,including random nutrient-phytoplankton models,random phytoplankton-zooplankton models,and random nutrient-phytoplankton-zooplankton models.Using stochastic differential equation theory and fuzzy set theory,we study the persistence and extinction,as well as the existence of ergodic stationary distribution,emphatically reveal the influence of environmental fluctuations on the survival of plankton,and further explore the mechanism of algal periodic blooms,thus providing a theoretical basis for controlling algal blooms.More precisely,the results are as follows:Firstly,based on bottom-up control mechanism,taking into account toxic algae,seasonal variation and nutrient cycling time delay,three kinds of random nutrientphytoplankton models with white noise are established.The conditions for the persistence and extinction of phytoplankton are obtained.The existence of stationary distribution and stochastic positive periodic solution is proved.Combined with the published data,the theoretical analysis is simulated numerically.The results show that toxin-producing phytoplankton and environmental fluctuations could affect the peak of algae outbreak and play a key role in its control.In addition,time delay only affects the convergence rate of phytoplankton,but does not change its stability.Secondly,based on top-down control mechanism,taking into account environmental pollution,toxic algae and parameter fuzziness,three kinds of phytoplankton growth models with uncertain factors are established.Survival of plankton in polluted environments is studied by Khasminskii theory,and the positive recurrence and ergodicity of stochastic models are proved.It is found that colored noise is beneficial to maintain the balance of the aquatic ecosystem,while white noise can increase the risk of species extinction.The spatial arrangement of random states near deterministic attractors is studied based on stochastic sensitivity functions technique,and the critical noise intensity leading to species extinction is estimated by using confidence ellipses.The numerical results show that the intermediate noise can produce complex dynamics and change the competition outcomes in many counterintuitive ways.The influence of fuzzy parameters on plankton dynamics is studied by means of fuzzy set theory.It is pointed out that the fuzziness of biological parameters can change the bionomic equilibrium and the optimal harvesting policy.Finally,based on bottom-up and top-down control mechanisms,taking into account nutrient cycling and seasonal variation,three kinds of random nutrient-phytoplanktonzooplankton models are established.Survival of plankton is studied,and existence of ergodic stationary distribution as well as stochastic positive periodic solution is proved.It is found that environmental noise may cause the local bloom of phytoplankton,which surprisingly can be used to explain the formation of algal blooms to some extent.Also,seasonality can induce periodic bloom of phytoplankton.