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

Yingkang Xie, Zhen Wang and Bo Meng
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Yingkang Xie: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Zhen Wang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Bo Meng: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2019, vol. 7, issue 9, 1-10

Abstract: 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.

Keywords: business cycle model; stability; time delay; time-fractional-order; Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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