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

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
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Mathematics 2019, 7(9), 846; https://doi.org/10.3390/math7090846
Received: 7 August 2019 / Revised: 10 September 2019 / Accepted: 12 September 2019 / Published: 13 September 2019
(This article belongs to the Special Issue Mathematical Economics: Application of Fractional Calculus)
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. View Full-Text
Keywords: business cycle model; stability; time delay; time-fractional-order; Hopf bifurcation business cycle model; stability; time delay; time-fractional-order; Hopf bifurcation
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Xie, Y.; Wang, Z.; Meng, B. Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function. Mathematics 2019, 7, 846.

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