Abstract:

The authors studied dynamics of the Rayleigh model with two discrete timedelays of the price.First using the linear stability method and the Nyquist criterion, we discussed the local stability of the system equilibrium point and the existence of Hopf bifurcation, then  used normal form
 and the center manifold theorem to determine the formula of the branch direction and branch stability of periodic solutions. In addition, in the model  codimension 2 branch can appear, and we gave the local area map of the parameter a-τ plane stable equilibrium point, finally, via numerical simulation we verified the theoretical analysis.

Key words: price Rayleigh equation, two delay, Hopf bifurcation; codimension two bifurcation； direction of bifurcation, stability, periodic solution