An Analysis Of The Hopf Bifurcation For Comprehensive National Strength Model With Delay

In recent years,some scholor have researched Comprehensive national strength model.In this paper,we input the delay into it, and analysis local properties of it comprehensively. The paper investigate mainly bifurcation problem in the modified model ,it consists of six sections.First section: Is the introduction , introduct why this model append delay;Second section: We obtain a group of conditions that guarantee the model have the local Hopf bifurcation;Third section: We study the distribution of the zeros of a exponential polynomial ,and give stability of the two steady state stability E₁,E₂;Fourth section: Basing on the normal form theory and the center manifold theorem, we derive the formula for determining the properties of the Hopf bifurcation,such as : the direction Hopf bifurcation and the stability of the bifuecating periodic solutions Cyclical solution stability;Fifth section: Using the global Hopf bifurcation theorem for FDE and Bendixson criterion for two-dimensional ordinary differential equation, we obtain the global existence of periodic solutions;Finally, in sixth, we has carried on the numerical simulations using Matlab to our obtained corresponding certain conclusions.