Study On Pattern Dynamics Of Linearly Coupled Planktonic Predation System

Plankton patchiness is a natural phenomenon widely observed in aquatic ecosystem,and the self-organization mechanism of plankton patchiness has been a hot topic in recent 50 years.Considering the vertical migration of plankton between water layers the study constructs a spatiotemporal dynamic model of a coupled plankton predation system,studying the self-organization and spatiotemporal dynamics of nested patchiness in the coupled system,revealing a new mechanism for the emergence of nested structures in plankton patchiness.The main research findings are as follows:(1)Based on amplitude equation analysis and numerical simulation,four nested pattern types were discovered,including hexagonal cold spot pattern,cold spot-strip mixed pattern,strip pattern,and hexagonal hot spot pattern in the study of spatiotemporal dynamics models of two-layer coupled plankton predator-prey systems;It was revealed that the dispersion curve with two peaks is the key to forming nested patterns,and as the critical Turing mode wavenumber ratio increases,the difference in patchiness size in the nested structure correspondingly increases,leading to more small patches nested in larger patches;Further research was conducted on the effects of cross diffusion and convection on the self-organization of nested patchiness,and it was found that cross diffusion significantly enhances the complexity of nested patchiness,such as leading to the generation of new nested patchiness called white eye patchiness.Convection can create a three-layer nested structure in planktonic patches,and the size of convection coefficient can regulate the formation mechanism of patchiness.(2)In the study of spatiotemporal dynamics models of multi-layer coupled plankton predator-prey systems,it was found that the coupled system,under the influence of Hopf instability and Turing instability mechanisms,can generate patches of different scales or types in each layer,revealing the self-organization of spiral wave hot spots,three-layer hot spot nested patterns,and the feature projection mechanism of nested pattern emergence;Studied the impact of changes in vertical migration rate of herbivorous planktonic animals,discovered synchronous and asynchronous phenomena and characteristics of temporal evolution and spatial distribution of planktonic patches,and revealed the multi-stable mechanism of the coupled system;Considering the differences in diffusion coefficient and growth coefficient between different water layers,the distribution of plankton patches and biomass oscillation characteristics along the water depth were studied,revealing the mechanism by which bottom layer phytoplankton became extinct while herbivorous phytoplankton relied on surface layer phytoplankton to maintain stability.The paper found the correlation mechanism between the vertical migration of plankton and the nested characteristics of patches,discussed the synchronous,asynchronous and multistable phenomena of the spatiotemporal evolution of plankton patches,revealed the self-organization mechanism of nested patchiness,and provided a new theoretical explanation for the complexity of plankton patchiness in aquatic ecosystem.