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A fractional-order hyper-chaotic economic system with transient chaos

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  • Yousefpour, Amin
  • Jahanshahi, Hadi
  • Munoz-Pacheco, Jesus M.
  • Bekiros, Stelios
  • Wei, Zhouchao

Abstract

We introduce for the first time a fractional-order hyperchaotic economic system. In this system, chaos generation depends upon the value of fractional-order. For certain fractional orders, a sustained regime of chaos is obtained. Also, the transient chaos phenomenon is detected for lower fractional orders. The dynamical behavior of the system is numerically investigated using bifurcations diagrams, basins of attraction, and Lyapunov exponents. Next, an adaptive terminal sliding mode control (ATSMC) with neural network estimator for finite-time stabilization and synchronization of the fractional-order system has been proposed. The radial basis function (RBF) neural network is used to achieve the estimation of the unknown function of the system. Also, the effects of external disturbances are fully taken into account with neural network estimator. The weights of the RBF neural network are updated based on the appropriate adaptation law. Using the fractional version of the Lyapunov stability theorem, the finite-time convergence of the closed-loop system has been proven. Finally, the new control technique is used for control and synchronization of the fractional-order hyperchaotic economic system. Simulation results illustrate the effectiveness of the proposed control scheme for uncertain fractional-order systems in the presence of external disturbances.

Suggested Citation

  • Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303352
    DOI: 10.1016/j.chaos.2019.109400
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    References listed on IDEAS

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    1. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    2. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    3. Sasakura, Kazuyuki, 1994. "On the dynamic behavior of Schinasi's business cycle model," Journal of Macroeconomics, Elsevier, vol. 16(3), pages 423-444.
    4. Lin, Tsung-Chih & Lee, Tun-Yuan & Balas, Valentina E., 2011. "Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 791-801.
    5. Tarasova, Valentina V. & Tarasov, Vasily E., 2017. "Logistic map with memory from economic model," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 84-91.
    6. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou, 2007. "Chaos in a new system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1203-1212.
    7. Jahanshahi, Hadi & Yousefpour, Amin & Wei, Zhouchao & Alcaraz, Raúl & Bekiros, Stelios, 2019. "A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 66-77.
    8. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    9. Fanti, Luciano & Manfredi, Piero, 2007. "Chaotic business cycles and fiscal policy: An IS-LM model with distributed tax collection lags," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 736-744.
    10. Bodo, Bertrand & Mvogo, Alain & Morfu, Saverio, 2017. "Fractional dynamical behavior of electrical activity in a model of pancreatic β-cells," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 426-432.
    11. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
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