The Cai model with time delay: Existence of periodic solutions and asymptotic analysis

The economic growth model with endogenous labor shift under a dual economy proposed by Cai (Applied Mathematics Letters 21, 774-779 (2008)) is generalized in this paper by introducing a time delay in the physical capital. By choosing the delay as a bifurcation parameter, it is proved that the delayed model has unique nonzero equilibrium and a Hopf bifurcation is proven to exist as the delay crosses a critical value. Moreover the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated in this paper by applying the center manifold theorem and the normal form theory.