Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System

On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.

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Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2019.11.009 ◽

2020 ◽

Vol 172 ◽

pp. 321-340 ◽

Cited By ~ 9

Author(s):

Shiva Eshaghi ◽

Reza Khoshsiar Ghaziani ◽

Alireza Ansari

Keyword(s):

Hopf Bifurcation ◽

Fractional Order ◽

Chaos Control ◽

Fractional Order System ◽

Order System ◽

Control And Synchronization ◽

Bifurcation Chaos

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Frequency domain modelling and control of fractional-order system for permanent magnet synchronous motor velocity servo system

IET Control Theory and Applications ◽

10.1049/iet-cta.2014.1296 ◽

2016 ◽

Vol 10 (2) ◽

pp. 136-143 ◽

Cited By ~ 38

Author(s):

Wei Yu ◽

YangQuan Chen ◽

Ying Luo ◽

YouGuo Pi

Keyword(s):

Permanent Magnet ◽

Frequency Domain ◽

Fractional Order ◽

Permanent Magnet Synchronous Motor ◽

Servo System ◽

Synchronous Motor ◽

Fractional Order System ◽

Order System ◽

And Control ◽

Motor Velocity

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The stability and control of fractional-order system with distributed time delay

IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society ◽

10.1109/iecon.2017.8217098 ◽

2017 ◽

Author(s):

Keyong Shao ◽

Xiaofeng Gu ◽

Guangyuan Yang

Keyword(s):

Time Delay ◽

Fractional Order ◽

Fractional Order System ◽

Order System ◽

Stability And Control ◽

Distributed Time Delay ◽

The Stability ◽

And Control

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Dynamics Analysis and Control of a Five-Term Fractional-Order System

Discrete Dynamics in Nature and Society ◽

10.1155/2018/8284121 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10

Author(s):

Li-xin Yang ◽

Xiao-jun Liu

Keyword(s):

Fractional Order ◽

Equilibrium Points ◽

Fractional Order System ◽

Phase Portraits ◽

Order System ◽

Bifurcation Diagrams ◽

Compound Structure ◽

Dynamical Properties ◽

The Stability ◽

And Control

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.

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Toolboxes and programs for fractional-order system identification, modeling, simulation, and control

2016 17th International Carpathian Control Conference (ICCC) ◽

10.1109/carpathiancc.2016.7501168 ◽

2016 ◽

Cited By ~ 7

Author(s):

Igor Podlubny ◽

Ivo Petras ◽

Tomas Skovranek ◽

Jan Terpak

Keyword(s):

System Identification ◽

Fractional Order ◽

Fractional Order System ◽

Order System ◽

Modeling Simulation ◽

Simulation And Control ◽

And Control

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Stability and Hopf bifurcation analysis of a biotic resource enrichment on a prey predator population in fractional-order system

10.1063/5.0053307 ◽

2021 ◽

Author(s):

Abiodun Ezekiel Owoyemi ◽

Ibrahim Mohammed Sulaiman ◽

Salisu Sadiya Muhammad ◽

Oluwatayo Olatunde Oni ◽

Olukayode Williams Okedokun

Keyword(s):

Hopf Bifurcation ◽

Fractional Order ◽

Bifurcation Analysis ◽

Fractional Order System ◽

Order System ◽

Predator Population ◽

Biotic Resource

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Complex Dynamics and Hard Limiter Control of a Fractional-Order Buck-Boost System

Mathematical Problems in Engineering ◽

10.1155/2021/5572840 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

Bo Yan ◽

Shaojie Wang ◽

Shaobo He

Keyword(s):

Fractional Order ◽

Complex Dynamics ◽

Adomian Decomposition Method ◽

Nonlinear Circuits ◽

Fractional Order System ◽

Order System ◽

Control Analysis ◽

Adomian Decomposition ◽

Current Limiter ◽

And Control

Chaos and control analysis for the fractional-order nonlinear circuits is a recent hot topic. In this study, a fractional-order model is deduced from a Buck-Boost converter, and its discrete solution is obtained based on the Adomian decomposition method (ADM). Chaotic dynamic characteristics of the fractional-order system are investigated by the bifurcation diagram, 0-1 test, spectral entropy (SE) algorithm, and NIST test. Meanwhile, the control of the fractional-order Buck-Boost model is discussed through two different ways, namely, the intensity feedback and the hard limiter control. Specifically, the hard limiter control can be realized using a current limiter in the circuit, where the current limiter device is applied to control the branch current. The results show that the proposed fractional-order system has complex dynamic behaviors and potential application values in the engineering field.

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