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

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.

Semi‐Analytical Solutions for the Diffusive Kaldor–Kalecki Business Cycle Model with a Time Delay for Gross Product and Capital Stock

“…A business cycle model is utilized to explain the working of economic laws and can also be utilized to predict investment status, yield, costs, and other important factors in the business economic model. Also, it can help practitioners avoid fluctuations [15].…”

Input-to-State Stability for Impulsive Gilpin-Ayala Competition Model With Reaction Diffusion and Delayed Feedback

“…D ELAYED ecosystem or reaction-diffusion ecosystem has been investigated for a long time (see, e.g. [1]- [4], [10], [12]- [14], [16] and the references therein). But most of the related literature only involved in the Neumann zero boundary value.…”

“…Besides, the delayed feedback model is introduced in this paper, for the larval individuals in the population often have a certain growth period, and only adults can participate in the food competition among populations. Such delayed feedback models are not only suitable for biological population competition model, but also common to other dynamic models ( [14]- [16]). In addition, Markov models can always simulate the competition systems of biological population with random factors and other dynamical systems ( [9], [17] ).…”

Unique Existence of Globally Asymptotical Input-to-State Stability of Positive Stationary Solution for Impulsive Gilpin-Ayala Competition Model with Diffusion and Delayed Feedback under Dirichlet Zero Boundary Value

“…Delayed ecosystem or reaction-diffusion ecosystem has been investigated for a long time (see, e.g. [1][2][3][4]10,[12][13][14]16] and the references therein). But most of the related literature only involved in the Neumann zero boundary value.…”

“…Besides, the delayed feedback model is introduced in this paper, for the larval individuals in the population often have a certain growth period, and only adults can participate in the food competition among populations. Such delayed feedback models are not only suitable for biological population competition model, but also common to other dynamic models ( [14][15][16]). In addition, Markov models can always simulate the competition systems of biological population with random factors and other dynamical systems ( [9,17]).…”