depreciation rate

The main aim of this work is to analyze the dynamics of a delayed business cycle model described by partial differential equations (PDEs) in order to take into account the depreciation rate of capital stock and the diffusion effect.  Firstly, the existence of solutions and the economic equilibrium are carefully studied.  Secondly, the local stability and the existence of Hopf bifurcation are established.  Finally, some numerical simulations are presented to illustrate the analytical results.