|
|
An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity |
Abderrahmane Abbes1,†, Adel Ouannas2, and Nabil Shawagfeh1 |
1 Department of Mathematics, University of Jordan, Amman 11942, Jordan; 2 Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria |
|
|
Abstract This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order. The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically. In particular, the zero equilibrium point stability is investigated to demonstrate that the discrete macroeconomic system exhibits chaotic behavior. Through using bifurcation diagrams, phase attractors, the maximum Lyapunov exponent and the 0-1 test, we verified that chaos exists in the new model with incommensurate fractional orders. Additionally, a complexity analysis is carried out utilizing the approximation entropy (ApEn) and C0 complexity to prove that chaos exists. Finally, the main findings of this study are presented using numerical simulations.
|
Received: 18 March 2022
Revised: 20 May 2022
Accepted manuscript online: 24 May 2022
|
PACS:
|
02.30.Oz
|
(Bifurcation theory)
|
|
02.30.Sa
|
(Functional analysis)
|
|
05.45.-a
|
(Nonlinear dynamics and chaos)
|
|
05.45.Pq
|
(Numerical simulations of chaotic systems)
|
|
Corresponding Authors:
Abderrahmane Abbes
E-mail: abder.abbes@gmail.com
|
Cite this article:
Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity 2023 Chin. Phys. B 32 030203
|
[1] Podlubny I 1999 Fractional Differential Equations vol. 198 (Elsevier) [2] Ostalczyk P 2015 Discrete Fractional Calculus: Applications in Control and Image Processing (Singapore: World Scientific Publishing) [3] Yan B, He S and Wang S 2020 Math. Probl. Eng. 2020 2468134 [4] Edelman M, Macau E and Sanjuan M 2018 Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives (Berlin: Springer Cham) pp. 147-71 [5] Gao F, Li W Q, Tong H Q and Li X L 2019 Chin. Phys. B 28 090501 [6] Liu C R, Yu P, Chen X Z, Xu H Y, Huang L and Lai Y C 2019 Chin. Phys. B 28 100501 [7] Ouannas A, Khennaoui A A, Momani S, Pham V T and El-Khazali R 2020 Chin. Phys. B 29 050504 [8] Yu Y J and Wang Z H 2013 Chin. Phys. Lett. 30 110201 [9] Wu J, Zhan X S, Zhang X H and Gao H L 2012 Chin. Phys. Lett. 29 050203 [10] Zhang D, Shi J Q, Sun Y, Yang X H and Ye L 2019 Acta. Phys. Sin. 68 240502 (in Chinese) [11] Shukla M K and Sharma B B 2017 AEU Int. J. Electron. Commun. 78 265 [12] Peng Y, He S and Sun K 2021 Results Phys. 24 104106 [13] Khennaoui A A, Ouannas A, Bendoukha S, Grassi G, Lozi R P and Pham V T 2019 Chaos Solitons Fractals 119 150 [14] Almatroud A O, Khennaoui A A, Ouannas A and Pham V T 2021 Int. J. Nonlinear Sci. Numer. Simul. 2021 [15] Ouannas A, Khennaoui A A, Momani S, Grassi G and Pham V T 2020 AIP Adv. 10 045310 [16] Yan S L 2019 Acta. Phys. Sin. 68 170502 (in Chinese) [17] Abbes A, Ouannas A, Shawagfeh N and Khennaoui A A 2022 Eur. Phys. J. Plus 137 1 [18] He Z Y, Abbes A, Jahanshahi H, Alotaibi N D and Wang Y 2022 Mathematics 10 165 [19] Wieland V and Wolters M H 2010 Econ. Theory 47 247 [20] Morgenstern O 1963 Limits to the Uses of Mathematics in Economics (Philadelphia: American Academy of Political and Social Science) [21] Allen R G D 1970 Macro-Economic Theory: A Mathematical Treatment (London: Macmillan) [22] Blanchard O 2018 Oxford Rev. Econ. Policy. 34 43 [23] Masson P 1999 J. Int. Money Finance 18 587 [24] Aldurayhim A, Elsadany A A and Elsonbaty A 2021 Fractals 29 [25] Xin B, Peng W and Kwon Y 2020 Physica A 558 124993 [26] Khennaoui A A, Almatroud A O, Ouannas A, Al-sawalha M M, Grassi G and Pham V T 2021 Discrete Contin. Dyn. Syst. B 26 4549 [27] Hu Z and Chen W 2013 Discrete Dyn. Nat. Soc. 2013 275134 [28] Chu Y M, Bekiros S, Zambrano-Serrano E, Orozco-López O, Lahmiri S, Jahanshahi H and Aly A A 2021 Chaos Solitons Fractals 145 110776 [29] Puu T 1986 Reg. Sci. Urban Econ. 16 81 [30] Atici F M and Eloe P 2009 Electron. J. Qual. Theory Differ. Equ. 3 1 [31] Abdeljawad T 2011 Comput. Math. Appl. 62 1602 [32] Puu T 1986 Reg. Sci. Urban Econ. 16 81 [33] Djenina N, Ouannas A, Batiha I M, Grassi G and Pham V T 2020 Mathematics 8 1754 [34] Wu G C and Baleanu D 2013 Nonlinear Dyn. 75 283 [35] Wu G C and Baleanu D 2015 Commun. Nonlinear Sci. Numer. Simul. 22 95 [36] Gottwald G A and Melbourne I 2016 Chaos Detection and Predictability (Berlin-Springer) pp. 221-247 [37] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297 [38] Ran J 2018 Adv. Differ. Equ. 2018 1 |
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|