Bifurcation analysis of a non-standard finite difference scheme for a time-delayed model of asset prices

In this paper, we apply a non-standard finite difference scheme to a time-delayed model of speculative asset markets and discuss the effect of time delay on the dynamics of asset prices. Firstly, the stability of the positive equilibrium of the system is investigated by analysing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcations occur when the delay passes a sequence of critical values. Then, the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived. Finally, some numerical simulations are given to verify the theoretical analysis.