Delayed feedback on the dynamical model of a financial system

We investigate the effect of delayed feedbacks on the financial model, which describes the time variation of the interest rate, the investment demand, and the price index, for establishing the fiscal policy. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Through numerical bifurcation analysis, we obtain the supercritical and subcritical Hopf bifurcation curves which support the theoretical predictions. Moreover, the fold limit cycle and Neimark–Sacker bifurcation curves are detected. We also confirm that the double Hopf and generalized Hopf codimension-2 bifurcation points exist.

Research highlights
► Effect of delayed feedbacks on the financial model.
► Proof on the occurrence of Hopf bifurcation by local stability analysis.
► Numerical bifurcation analysis on delay differential equations.
► Observation of supercritical and subcritical Hopf, fold limit cycle, Neimark–Sacker, double Hopf and generalized Hopf bifurcations.