Stability Analysis Of Nonlinear Behavior Of Marine Plankton In Different Environments

Plankton not only provides food for marine mammals and commercially important fish,but also plays a fundamental role in the functioning of marine ecosystems by providing half of the global primary productivity and making a significant contribution to the biogeochemical cycle.Therefore,the change of marine plankton community is a problem worthy of attention.Biologically,the community structure of plankton is affected by many factors through the observation of marine survey data and experimental phenomena.Mathematical modeling is an important theoretical method for analyzing the effects of external environmental changes and internal physiological changes on plankton biomass.The growth of plankton can be predicted by establishing an appropriate mathematical model for plankton and studying the law of its biomass change.This thesis investigates the effects of different environments on the stability of plankton,including chemical and physical conditions(temperature,nutrients),biological processes(growth conditions,predatory environment),and adaptive changes(phenotypic plasticity,behavioral selection),which makes the problems studied in this thesis more realistic.For the predator-prey models with the adaptive changes and environmental factors,the dynamic behavior analysis of plankton model has been realized by stability theory and center manifold theorem.The main contents of this thesis are as follows:First,in order to study the changes of plankton biomass with different body sizes,the stability of a type of plankton model with cell size is considered,in which the growth rate and the sink rate of phytoplankton are functions of cell size,and the body size of zooplankton has the best predator-prey size ratio.On the basis of the positive definiteness and boundedness of the solution,the stability of the solution is studied and the Hopf bifurcation analysis is carried out.It is found that the relatively small plankton is more adaptable to the living environment in the evolution process,which is consistent with the empirical model of marine phytoplankton.Second,based on the previous study,considering the impacts of internal conditions of or-ganisms and external environment on plankton,the steady distribution of a stochastic nutrient-plankton model with body size is studied.The body sizes determine the adaptability of phyto-plankton and zooplankton.The growth rate,nutrient ratio and sink rate of phytoplankton are restricted by cell size.The nutrient ratio and consumption rate of zooplankton are related to its bosy size,and the loss rate of nutrient,the mortality rates of phytoplankton and zooplank-ton are affected by the external environment.On the basis of the existence and uniqueness of the global positive solution with positive initial values,the sufficient conditions for the existence of ergodic stationary distribution of positive solutions are constructed.Through analysis,it is found that large noise interference will lead to the extinctions of phytoplankton and zooplankton.Thirdly,considering the effect of spatiotemporal delay,a diffusive plankton model re-stricted by the Neumann boundary condition is considered.By transforming the two-dimensi-onal model with spatiotemporal delay into a three-dimensional model,the local and global stability of the positive steady-state solution are discussed.Secondly,by using the maximum principle and Harnack inequality,a priori estimate of positive nonconstant steady states is given.In addition,the sufficient conditions for the nonexistence and existence of the posi-tive nonconstant steady states of the reaction-diffusion model are established,indicating that zooplankton diffusion with a large diffusivity will lead to the generation of stationary pat-terns.Then,the effects of phytoplankton defense and zooplankton offense on the plankton model are studied,in which the intrinsic growth rate of phytoplankton is a function of phytoplankton defense,the capture rate of zooplankton is determined by the levels of the defense and offense,and the conversion efficiency of phytoplankton is affected by the offense.Based on the analysis of Truing instability and Hopf bifurcation of spatial diffusive model,it is found that diffusion leads to Turing instability,while the strength and weakness of defense and offense will lead to the oscillation of plankton populations.Finally,the influence of water temperature on the stability of plankton model is studied by establishing the functions of model parameter on the water temperature.In the physio-logical related temperature range,the relationships between temperature and plankton model parameters are simulated as hump type and U type,respectively,and the functional response Holling parameter is generalized.Through stability analysis and numerical simulation,it is revealed how the dynamic behavior of the model evolves when the parameters are close to the threshold value at different water temperatures,which can be regarded as a prediction of plankton diversity under high temperature.To sum up,the stability of the plankton model under different environments studied in this thesis has realized the practicality of the model to a certain extent,enriched the theoretical knowledge of plankton,and also has a certain predictive effect on the changes of plankton population under more complicated situations.