Study On The Diffusion Dynamics Of Phytoplankton In Fixed And Evolutionary Regions

Phytoplankton are microorganisms in aquatic ecosystems.Using the external energy provided by the sun,they convert mineral nutrients into primitive biomass.They constitute the bottom of the food web in aquatic ecosystems such as oceans,lakes and reservoirs,and play an important role in aquatic ecosystems and climate changing.However,the outbreak of phytoplankton has negative effect on ecosystems and socio-economic.Therefore,it is necessary to understand the dynamic of phytoplankton.This paper mainly explores the impact of the domain evolution on the dynamic of phytoplankton by studying the reaction-diffusion model of nutrient-phytoplankton in a fixed domain and a periodically evolving domain.The full text is divided into four chapters.The first chapter mainly introduces the historical development and current research situation of the nutrient-phytoplankton model and the related problems about evolving domain.We present the problem to be studied in this paper,and state the main contents of this paper.In the second chapter,we study the reaction-difiusion model of phytoplankton in the periodically evolving domain under the condition of a constant input rate of nutrient.The asymptotic behavior of the model is obtained by using the corresponding eigenvalue problem and the upper and lower solution method.According to the conclusion,we use Matlab to simulate the phytoplankton model on the periodically evolving domain,and verify our theoretical results by the graph drawn.Finally,we further give an ecological explanation for the impact of domain evolution on the growth of phytoplankton.In the third chapter,the constant-coefficient nutrient-phytoplankton model in a fixed domain is studied.Firstly,the ecological reproduction index is introduced,and the stability of the boundary equilibrium and the positive equilibrium are given by using the classical theory of partial differential equation.Then,the nutrient-phytoplankton model in a fixed area is simulated by mathematical software,and the theoretical results are explained.Chapter IV summarizes the main conclusions of the issues given in this paper,and makes further explanations from the perspective of ecology.Finally,we put forward some problems to be studied and explored in the future.