Hopf Bifurcation Analysis of a Continuous Investment Update Project Model

Abstract

Some investment projects aim not only to produce goods but more importantly, to update and efficiently supply products in accordance with market demand. A double time delay differential dynamics model is formulated for continuous renewal investment projects based on the flowchart of the capital appreciation process and the assumed transfer functions. By analyzing the mathematical model, it can be determined that a unique local asymptotically stable positive equilibrium point exists for the continuous investment project. In accordance with the Hopf branching theorem, the model displays periodic behavior in proximity to its positive equilibrium point under certain conditions. The simulation results are compared under various conditions, and the validity of the relevant conclusions is confirmed.