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Dynamic analysis and adaptive modified projective synchronization for systems with Atangana-Baleanu-Caputo derivative: A financial model with nonconstant demand elasticity

Author

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  • Lin, Xiaoran
  • Wang, Yachao
  • Wang, Jifang
  • Zeng, Wenxian

Abstract

The inherent instability of the financial system itself may lead to chaos and unpredictable economic disorder. It is meaningful to study the stability and control theory of financial chaotic system. Based on the definition of Atangana-Baleanu-Caputo fractional derivative, this work extends the integer-order financial chaotic system with nonconstant demand elasticity to a fractional-order system, and analyzes its nonlinear dynamic properties. The dynamic behavior of the system is discussed by phase diagram, bifurcation diagram, the Largest Lyapunov Exponent (LLE) and 0–1 test method. An adaptive controller is designed to realize the modified projection synchronization of the system. The results can help to improve the understanding of the complex financial system, and provide theoretical support for the formulation of financial intervention strategies.

Suggested Citation

  • Lin, Xiaoran & Wang, Yachao & Wang, Jifang & Zeng, Wenxian, 2022. "Dynamic analysis and adaptive modified projective synchronization for systems with Atangana-Baleanu-Caputo derivative: A financial model with nonconstant demand elasticity," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004799
    DOI: 10.1016/j.chaos.2022.112269
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    References listed on IDEAS

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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    2. Panas, E., 2001. "Long memory and chaotic models of prices on the London Metal Exchange," Resources Policy, Elsevier, vol. 27(4), pages 235-246, December.
    3. Xiaoran Lin & Yachao Wang & Guohao Wu & Jing Hao & Zakia Hammouch, 2021. "Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, April.
    4. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
    5. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    6. Mohammed Salah Abd-Elouahab & Nasr-Eddine Hamri & Junwei Wang, 2010. "Chaos Control of a Fractional-Order Financial System," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-18, July.
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