Research progress in rice blast resistance gene Pita and Pib of indigenous rice cultivars in Yunnan

A class of natural pest-enemy system with time delays is considered,where the time delay is regarded as bifurcation parameter.By analyzing the corresponding characteristic equation,the local stability of equilibriums is investigated.Moreover,we show that Hopf bifurcations occurs when time delay crosses some critical values.A numerical simulation is carried out to illustrate the theoretical results.