Dynamic Analysis of the Project Investment Model with Time Delay and Density Constraints

The purpose of research, invention, and production is to effectively supply demand, which requires not only financial support but also time to complete. First, the differential dynamic model among funds, demand, and research (including invention and production) with time delay is constructed by using the predator-prey theory. Second, the sufficiency of local asymptotic stability of the positive equilibrium point of the model is obtained by using the Hopf bifurcation theory and stability theory. Then, the formulas for determining the direction of Hopf bifurcation and the stability of the periodic solution are calculated by using the central manifold theory and normative theory. Finally, the evolution process of the differential dynamic model with controlled time delay is numerically simulated so as to verify the correctness of the relevant analytical conclusions.