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Oligopolies price game in fractional order system

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  • Li, Yaguang
  • Sun, Chunhua
  • Ling, Haifeng
  • Lu, An
  • Liu, Yezheng

Abstract

A new fractional discrete dynamical system of the price game model is proposed by considering long-term memory of price volatility based on the discrete fractional differentiation calculus. The complex dynamic behaviours are studied with various differential orders using bifurcation diagrams of price. The numerical simulation has indicated that long periods of price adjustment are needed to achieve a stable region as the fractional order decreases, whilst the dynamic behaviours of bifurcation and chaos become increasingly complex. The fractional system, that is more generalized than the integer-order, is stable on the low-price adjustment speed and generally chaotic on the fast-price adjustment speed. This study uses the parameter-dependent Lyapunov stability theory as basis to address the tracking errors for a fractional discrete dynamical system by controllers. When bifurcation and chaos exist in fractional discrete dynamical system, the controllers are presented to guarantee that the actual value prices converge to the expected value prices.

Suggested Citation

  • Li, Yaguang & Sun, Chunhua & Ling, Haifeng & Lu, An & Liu, Yezheng, 2020. "Oligopolies price game in fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305405
    DOI: 10.1016/j.chaos.2019.109583
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    References listed on IDEAS

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    1. Abdeljawad, Thabet & Baleanu, Dumitru, 2017. "Monotonicity analysis of a nabla discrete fractional operator with discrete Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 106-110.
    2. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    3. Gallegos, Javier A. & Duarte-Mermoud, Manuel A., 2016. "On the Lyapunov theory for fractional order systems," Applied Mathematics and Computation, Elsevier, vol. 287, pages 161-170.
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    1. Grau-Climent, Juan & Garcia-Perez, Luis & Alonso-Sanz, Ramon & Losada, Juan C., 2023. "Effect of players’ expectations and memory in a quantum Cournot game," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Xi, Xuan & Zhang, Jixiang, 2020. "Complexity analysis of a decision-making game concerning governments and heterogeneous agricultural enterprises with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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