Hopf Bifurcation of A Kaldor-Kalecki Business Cycle Model with Variable Depreciation Rate and Diffusion Effect

A Kaldor-Kalecki business cycle model with variable depreciation rate and diffusion effect is proposed in this study. Nowadays, most present researches about Kaldor-Kalecki model regard the depreciation rate as constant. However, in practical business cycle model, depreciation rate is variable and related to many aspects. The paper further considers the impact of the gross product on depreciation rate, which describes actual economic model more accurately. The local stability at equilibrium point and the existence of Hopf bifurcation are analyzed. It is obtained that the dynamic behaviors depend on the critical value of bifurcation. Moreover, some conditions to ensure the stability and some criteria of Hopf bifurcation are obtained. Finally, examples and simulations are given to illustrate the correctness of the theoretical results.