Dynamical analysis for a model of asset prices with two delays

• Bifurcation analysis is employed to study the market stability or oscillation.
• Use center manifold reduction method to investigate the stability and criticality.
• Delay induces supercritical bifurcation and makes oscillating period increase.

This paper provides a new perspective to understand the mechanism on the market stability or oscillation by investigating a two-dimensional asset price model with two delays. Stability conditions and the existence of Hopf bifurcation are obtained by investigating the characteristic equation. Then an explicit algorithm for determining the criticality of Hopf bifurcation and stability of the bifurcating solutions is derived, using the center manifold reduction method. The global continuation of bifurcating periodic solutions is detected using a global Hopf bifurcation theorem. It is found that delay may induce supercritical Hopf bifurcations, hence bring oscillation into the asset price model. Moreover, when time delay gets larger, the period of oscillation also increases. Finally, some numerical illustrations with Matlab and DDE-Biftool are carried out to support the theoretical analysis.