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Complex Dynamical Behaviors in a Dual Channel Supply Chain Model with Retailer’s Service Input

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Abstract

Based on bounded rationality, this paper established a price game model of dual channel supply chain composed of manufacturers and retailers. According to the eigenvalue of Jacobi matrix and Jury criterion, the stability of the equilibrium point is analyzed, and then the dynamic evolution process under the parameters of price adjustment speed and retailer’s service input is studied through stability region, bifurcation diagram, maximum Lyapunov exponent diagram and attraction basin. The results show that the system enters chaos through flip and Neimark-Sacker bifurcation, and increase of price adjustment speed and service input value will make the system produce more dynamic behavior. In addition, it can be found that the impact of service input value on itself is much greater than that on manufacturers. Secondly, when adjustment speed is selected as bifurcation parameter, the change curve of sales price is inconsistent, in which the change of retailers mainly remains in periodic state, while manufacturers will gradually enter chaos. Finally, studies the evolution of attraction basin in which three kinds of attractors coexist. In particular, coexistence of boundary attractors and internal attractors increases the complexity of system. Therefore, enterprises need to carefully adjust parameters of the game model to control the stability of system and maintain the long-term stability of market competition.

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Author information

Authors and Affiliations

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Yapeng Zhang

  2. School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Wei Zhou

  3. Key Laboratory of Railway Industry of Plateau Railway Transportation Intelligent Management and Control, Lanzhou, 730070, China

    Wei Zhou

Authors
  1. Yapeng Zhang
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  2. Wei Zhou
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Correspondence to Wei Zhou.

Additional information

This research was supported by the Foundation of a Hundred Youth Talents Training Program of Lanzhou Jiaotong University, the Innovation Fund Project of Colleges and Universities in Gansu Province under Grant No. 2021A-040.

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Zhang, Y., Zhou, W. Complex Dynamical Behaviors in a Dual Channel Supply Chain Model with Retailer’s Service Input. J Syst Sci Complex 36, 1144–1168 (2023). https://doi.org/10.1007/s11424-023-1209-x

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  • DOI: https://doi.org/10.1007/s11424-023-1209-x

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