Research On Ecological Models Of Several Types Of Belt Capture

In this paper,we use the method of dynamical system to study the biological dynamics of two kinds of common model:the predator-prey model with prey's growth subject to power law and the coral reef ecosystem model that considers the competition within the corals.In the predator-prey model,the functional response function of the predator-prey model is chosen as the Holling-? type,and with constant capturing.We select constant capturing rate h and predators conversion b as parameters,through calculating the Jacobian matrix near the equilibrium points and its eigenvalues,together with Hartman-Grobman Theroem to get the types and stability of the equilibrium points,and calculating the normal form near the equilibrium points to study the hopf bifurcation.Finally,by using matlab software to carry on the numerical simulation,and the conclusions are consistent with the actual data.In the coral reef ecosystem model,we consider internal competition between the coral reefs.We select the grazing rate of the herbivorous g as the parameter,through calculating the Jacobian matrix near the equilibrium points,and its eigenvalues,together with Hartman-Grobman Theroem to get the types and stability of the equilibrium points,and using Sotomayor's Theorem to study the saddle node bifurcation and the transcritical bifurcation.