On the equilibrium point and Hopf-Bifurcation analysis of GDP-national debt dynamics under the delayed external investment: A new DDE model

This mathematical model is based on a system of two non-linear delay differential equations representing GDP (Gross Domestic Product) growth and national debt respectively. Growth of GDP is directly proportional to national debt. In the absence of national debt, there could be no or very slow GDP growth. The national debt is heavily dependent on external loans and external investments. These investments act as a catalyst for accelerating the rate of GDP. It is assumed that the external debt is never paid off fully. The availability of external investments is not immediate as per demand but takes some time for the maturation of the deal. The time delay in actual arrival of the foreign investment and its effect on GDP-National debt dynamics is the main focus of this study. This effect is studied using a delay parameter τ. The non-zero equilibrium of the system is calculated, and the stability analysis is performed on it. Hopf bifurcation is observed for a critical value of the delay parameter. Numerical simulation is performed using MATLAB code.