Stability and bifurcation analysis of a financial dynamical system with time delay

This work proposes a new mathematical model incorporating the interest rate, investment demand, price index, profit margin, and time-delay feedback factor. The linear stability of the system at each of the existing equilibria is examined, and it is found that the system undergoes a Hopf bifurcation through changing stability to instability around the equilibria due to the time-delay feedback factor. All the theoretical findings have been verified numerically, highlighting the impact of time delay and the influences of various factors such as savings amount, profit sensitivity, margin adjustment, and elasticity of demand on the stability of a financial system.