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Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation

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  • Li, Yan
  • Wang, Lidong

Abstract

In this paper, we construct a duopoly model of technological innovation based on constant conjectural variation under the assumption of bounded rationality. The equilibrium points of constant conjectural variation and their local stability are investigated. By the theoretical proof, we prove that the model displays Li-Yorke chaos and distributional chaos in the ranges of the output adjusted coefficients by employing the snap-back repeller theory. The technological innovation is the main source of the core competitiveness of a firm, and technological content is an important factor of technological innovation. We find that the firms have the optimal technological contents while they could have the maximal profits in the two different situations, non-cooperative technological innovation and cooperative technological innovation. It’s proved that the cooperation of technological innovation can increase the marginal technological content, and benefit to technological progress. Then Numerical simulations are used to illustrate the dynamic analysis of the model under the situations with different technological innovation and conjectural variation. When the output adjusted coefficient changes, a series of complex phenomena including bifurcation, chaos and strange attractor can be observed in our model. And when the technological content is larger, the chaos of the system finally appears.

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  • Li, Yan & Wang, Lidong, 2019. "Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 116-126.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:116-126
    DOI: 10.1016/j.chaos.2018.11.038
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    Cited by:

    1. Li, Hui & He, Ruichun & Zhou, Wei, 2022. "Dynamic behaviors in a Cournot duopoly model with knowledge spillover effect based on constant conjectural variation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 305-323.
    2. Ismael Cristofer Baierle & Francisco Tardelli da Silva & Ricardo Gonçalves de Faria Correa & Jones Luís Schaefer & Matheus Becker Da Costa & Guilherme Brittes Benitez & Elpidio Oscar Benitez Nara, 2022. "Competitiveness of Food Industry in the Era of Digital Transformation towards Agriculture 4.0," Sustainability, MDPI, vol. 14(18), pages 1-22, September.
    3. Askar, S.S. & Al-khedhairi, A., 2020. "The dynamics of a business game: A 2D-piecewise smooth nonlinear map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Garmani, Hamid & Ait Omar, Driss & El Amrani, Mohamed & Baslam, Mohamed & Jourhmane, Mostafa, 2020. "Analysis of a dynamics duopoly game with two content providers," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Sameh Askar, 2021. "Complex Investigations of a Piecewise-Smooth Remanufacturing Bertrand Duopoly Game," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    6. Sameh S. Askar, 2020. "A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit," Mathematics, MDPI, vol. 8(10), pages 1-13, October.

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