Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function

Mathematics

Zhen Wang¹  Yingkang Xie¹  Bo Meng¹ 

[1] College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;

关键词: business cycle model;    stability;    time delay;    time-fractional-order;    Hopf bifurcation;   

DOI  :  10.3390/math7090846

来源: DOAJ

【 摘 要 】

In this paper, the business cycle (BC) is described by a delayed time-fractional-order model (DTFOM) with a general liquidity preference function and an investment function. Firstly, the existence and uniqueness of the DTFOM solution are proven. Then, some conditions are presented to guarantee that the positive equilibrium point of DTFOM is locally stable. In addition, Hopf bifurcation is obtained by a new method, where the time delay is regarded as the bifurcation parameter. Finally, a numerical example of DTFOM is given to verify the effectiveness of the proposed model and methods.

【 授权许可】

Unknown