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Volume 2018, Article ID 1263602, 11 pages
Research Article

Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect

Wenjie Hu,1,2 Hua Zhao,1,3 and Tao Dong4

1College of Economics and Business Administration, Chongqing University, Chongqing 400030, China
2College of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
3School of Management, Chongqing Technology and Business University, Chongqing 4000067, China
4College of Electronics and Information Engineering, Southwest University, Chongqing 400715, China

Correspondence should be addressed to Hua Zhao; nc.ude.uqc@auhoahz

Received 5 April 2017; Accepted 6 December 2017; Published 9 January 2018

Academic Editor: Dimitri Volchenkov

Copyright © 2018 Wenjie Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear.