Self-organization Behaviors Of Marine Plankton In Different Environments

Phytoplankton are the primary producers in the marine biosphere,and zooplankton the primary consumers,together they constitute plankton micro ecosystems which are the origin of the marine food webs.When there are too many phytoplankton,algal blooms occur,which seriously affects the marine biodiversity,destroys the flows of marine material and energy,weakens the stability of the marine ecosystem,and impacts humans' life and production.Therefore,it is of great significance to study the properties of the plankton ecosystems,especially the spatiotemporal distribution of the plankton,to explore the evolution of the plankton ecosystems,and to explain the related ecological phenomena.This paper mainly researched the self-organization behaviors of the plankton.The reaction-diffusion equations were used to model the plankton systems,composed of phytoplankton and zooplankton,in different environments.Through stability analysis,bifurcation analysis,and weakly nonlinear analysis,the properties of the plankton systems,such as the stability of the reaction equations,Turing bifurcation,Turing-Hopf(TH)bifurcation,self-organization patterns,and traveling patterns,were studied.The researches and results are as follows:First,I researched the effects of group predation and weakly nonlinear diffusion on the self-organization of a plankton ecosystem.The zooplankton form small groups,cooperatively forage phytoplankton,and disperse nonlinearly to adapt to the group predation and to avoid fierce interspecific competition.By the stability analysis,I got the stability condition of the reaction equations and the Turing bifurcation.Then,the weakly nonlinear analysis helped me get the types of patterns because of the diffusion rate of zooplankton.As the diffusion coefficient of the zooplankton increases within the "Turing pattern zone",the plankton tend to gather and form high density patches.At last,the numerical simulations illustrated the self-organization behaviors of the plankton.Second,I researched the effects of the herd-taxis on the self-organization of a plankton community.The zooplankton have herd-taxis depicted by the nonlinear cross-diffusion.I chose the ratio-depend type function response and built a plankton model by the reaction-nonlinear diffusion equations.The stability analysis gave out the stability condition of the reaction equations and the Turing bifurcation,and implied that the herd-taxis of the zooplankton helps to smooth the inhomogeneous distribution of the plankton.Then the weakly nonlinear analysis contributed to exploring the effect of herd-taxis on the self-organization and the types of Turing patterns,which showed that the active forage tends to weaken the gather of the plankton and eliminate the high density plankton patches.The study showed that some reaction-nonlinear diffusion equations can be dealt with by the weakly nonlinear analysis without linearizing the nonlinear diffusion.Third,I researched the self-organization behaviors of the plankton community in which the zooplankton prey phytoplankton non-locally.The plankton micro ecosystem with nonlocal predation is modeled by an integro-differential equations.Through the stability analysis,I got the Hopf bifurcation,the Turing bifurcation,the codimension-2 Turing-Hopf(TH)bifurcation,and the conditions for the strong/weak TH instability.Furthermore,the weakly nonlinear analysis helped to explore the types of patterns as the zooplankton disperse faster.And the numerical simulations implied the variation of the Turing bifurcation and patterns of different types because of the hunter function.The analyses meant that the plankton tend to gather and form high-density patches as the zooplankton forage more dispersedly or diffuse faster.The study showed the application of the weakly nonlinear analysis to the nonlocal reaction-diffusion equations(integral differential equations).Final,I researched the effects of the advection on the self-organization of a plankton community.In the sea,ocean currents carry plankton ecosystems,and the phytoplankton,as well as the zooplankton,float at different or the same speed due to their physical properties.If the advection velocities of all plankton are the same,the plankton community remains relatively stationary.If the convection velocities are different,the speed difference may drive the system unstable.When the reaction-diffusion(RD)system is Turing stable,due to the advection speed difference,there should be a wave bifurcation which could drive the advectionreaction-diffusion(ARD)system wave instability.If the RD system becomes Turing unstable,the ARD system will always be of wave instability.Numerical simulations validated my analysis and showed more phenomena.When the RD system is Turing unstable,we keep the advection speed of the phytoplankton zero and the zooplankton nonzero,If the speed difference is small enough,the patterns remain stationary,and if the speed difference increases,the traveling patterns appear.Therefore,there should be a traveling bifurcation that separates the stationary patterns and the traveling ones.In conclusion,this paper focused on the effects of several biological and environmental factors on the self-organization of the plankton communities and analyzed the spatiotemporal dynamics of the plankton ecosystems under different conditions,which enriched the researches on the self-organization of the plankton ecosystems.Besides,I expanded the application scope of the weakly nonlinear analysis and applied the tool to the reaction-nonlinear diffusion equations and the nonlocal reaction-diffusion equations.