Dynamical Analysis In NICHOLSON Blowflies Equation With Two Delays

It's easy to carry out experiment about blowflies because of their short reproductive cycle. So lots of researches have been done about the blowflies equation in both mathematics and biology, and it's Nicholson's model which is discussed mostly.In this paper, the kinetic properties of Nicholson's blowflies equation with two delays and harvesting rate is investigated. shows the period of the organisms from larvae to the time when they can be captured. And H is the intensity coefficient. In our paper, the stability of equilibrium point together with the existence and stability of local Hopf bifurcation are discussed in detail.Firstly, we introduce briefly the development of differential equations and what we do in the paper. Then we will linearize the model and discuss the system with one delay and two delays respectively. And we can obtain the distribution of the characteristic roots, the stability of the equilibrium, the existence of local Hopf bifurcation and its conditions. Secondly, using center manifold theory and normal form method, we can give the formulas of the local Hopf bifurcation to discuss the direction of the bifurcation, the stability of bifurcating periodic solutions and the period of the solutions. At last, by means of computer and MATLAB program, some simulations will be given to support the theoretical results obtained previously. What's more, taking as the parameter and using MATLAB software, we may also get the stability switch phenomenon near the positive equilibrium point.The last part is the conclusion, in which the main results of the paper are summarized.