Dynamic Mechanism On Spatial Diffusion Of Several Marine Plankton Populations

This paper mainly studies the nonlinear dynamics of several marine plankton systems.Through the discussion of the hot spots in the system,some important conclusions are summarized.In chapter 1,the introduction part briefly introduces the research background and research status of marine plankton system.In addition,we presented some basic definitions and important lemmas which are frequently used in the following chapters.In chapter 2,the dynamics of a marine phytoplankton-zooplankton system with diffusion are investigated.Based on theoretical proofs,we determine some conditions for the local and global stability,such as Turing instability in the ecological model.Numerical studies not only verity the correctness of the theoretical results,also determine the relationships between pattern formation and the diffusion and the environmental carrying capacity.The results demonstrate that diffusion and the environmental carrying capacity may influence the interaction between phytoplankton and zooplankton.In chapter 3,a ecological population nonlinear system with diffusion which described the interaction between the toxin producing phytoplankton and zooplankton are discussed analytically.By the theoretical analysis,we find that the equilibrium will lose its stability via Turing instability and pattern formation will occur.Especially,the analysis indicated that the cross-diffusion can play an important role in the pattern formation.The numerical simulations showed that the rich dynamics induced by the diffusion in the system,and simulations further represent that the direction of cross-diffusion can influence the spatial distribution of population and population density.In chapter 4,the dynamical properties of a toxic phytoplankton-zooplankton ecological population system are studied.Through theoretical analysis and proof,we find that the stability transition of the system cannot occur when the effect of self diffusion is considered.It is proved that the local and global stability of the system cannot be guaranteed when the self diffusion and cross diffusion are combined.It reveals that the cross diffusion will obviously affect the stability of the system through the comparison of the results.