Asmptotic Behavior On Several Types Of Coral Reef Ecosystem

The coral reef ecosystem with reef-building corals as the core is a unique underwater ecosystem,which can maintain the diversity of Marine life.The coral reef ecosystem can provide abundant Marine products,chemicals and medicines for human beings,and have great value for ecological sightseeing as well.Reef-building corals are mainly affected by macro-algae,urchin and grass-eating fish.On the one hand,macro-algae compete with symbiotic zooxanthellae in coral coelom for photosynthesis;on the other hand,sea urchin contribute to the growth of corals by feeding on macro-algae.In the past decade,sea urchin and herbivorous fish populations have declined due to infectious diseases and overfishing,leaving corals at a vulnerable position in competition with large algae and further exacerbating the crisis.The aim of this paper is to establish a mathematical model of coral reef ecosystem by means of ordinary differential equations.We study the dynamic properties by means of qualitative theory,and we explore the internal mechanism of coral reef ecosystem health in theory.This paper is divided into four chapters.In the second chapter,a mathematical model is established based on the ecological relationship among coral,algae,sea urchin and turf algae.We study the boundedness and positive invariance of system solutions,as well as the number of equilibrium stability and other issues by means of qualitative theory.In the third chapter,we add grass-eating fish to the above model.According to the relationship between grass-eating fish,coral,algae,sea urchin and turf algae,we detailed study positive invariance of system solutions,boundedness,branching,the stability of the equilibrium and so on.In this paper,we use Sotomayor's branch theorem,Routh-Hurwitz theorem,etc.