Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(3): 030203    DOI: 10.1088/1674-1056/ac7296
GENERAL Prev   Next  

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.
Keywords:  chaos      macroeconomic system      discrete fractional calculus      complexity  
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:

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
[1] Unstable periodic orbits analysis in the Qi system
Lian Jia(贾莲), Chengwei Dong(董成伟)†, Hantao Li(李瀚涛)‡, and Xiaohong Sui(眭晓红). Chin. Phys. B, 2023, 32(4): 040502.
[2] A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain
Chunlei Fan(范春雷) and Qun Ding(丁群). Chin. Phys. B, 2023, 32(1): 010501.
[3] Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability
Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[4] Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map
Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[5] Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback
Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Chin. Phys. B, 2022, 31(7): 074205.
[6] Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation
Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[7] Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network
Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Chin. Phys. B, 2022, 31(2): 020502.
[8] Energy spreading, equipartition, and chaos in lattices with non-central forces
Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Chin. Phys. B, 2022, 31(2): 020506.
[9] Resonance and antiresonance characteristics in linearly delayed Maryland model
Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[10] An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree
Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). Chin. Phys. B, 2022, 31(11): 110503.
[11] Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system
Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(1): 010501.
[12] Control of chaos in Frenkel-Kontorova model using reinforcement learning
You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Chin. Phys. B, 2021, 30(5): 050503.
[13] Dynamics analysis in a tumor-immune system with chemotherapy
Hai-Ying Liu(刘海英), Hong-Li Yang(杨红丽), and Lian-Gui Yang(杨联贵). Chin. Phys. B, 2021, 30(5): 058201.
[14] Resistance fluctuations in superconducting KxFe2-ySe2 single crystals studied by low-frequency noise spectroscopy
Hai Zi(子海), Yuan Yao(姚湲), Ming-Chong He(何明冲), Di Ke(可迪), Hong-Xing Zhan(詹红星), Yu-Qing Zhao(赵宇清), Hai-Hu Wen(闻海虎), and Cong Ren(任聪). Chin. Phys. B, 2021, 30(4): 047402.
[15] Efficient self-testing system for quantum computations based on permutations
Shuquan Ma(马树泉), Changhua Zhu(朱畅华), Min Nie(聂敏), and Dongxiao Quan(权东晓). Chin. Phys. B, 2021, 30(4): 040305.
No Suggested Reading articles found!