Modeling And Research Of Several Types Of Coral Reef Ecosystems

This paper is based on the mathematical model of coral reef ecosystem in the Caribbean Sea,which is established by P.Mumby et al.in “Nature” in 2007.We improved and established an ordinary differential equation model related to the actual activity of coral planting in the South China Sea by Chinese scientists.In Chapter 1,qualitative theory and bifurcation theory are employed to study the dynamical behavior of the system.Noting that the number of the equilibriums and their stability depend on the value of each parameter sensitively,the basic research results indicate that when the parameters of coral cultivation are not large enough,the coral reef ecosystem tends to become extinct;when the parameters increase to a certain extent,the stable state tends to be beneficial to coral growth and can achieve a stable coexistence situation of coral reef and microalgae.In Chapter 2,we assume that macro algae is not overgrazed until it grows high enough.So we add a time delay in the system.By investigating the distribution of the eigenvalues of the Jocobian Matrix we discuss the stability of the equilibrium points.Chapter 3 focuses on the diffusion impact to the ecosystem.We establish sufficient conditions to ensure Turing instability appears for certain equilibrium.