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The equilibrium, complexity analysis and control in epiphytic supply chain with product horizontal diversification

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Abstract

The dynamic of an epiphytic supply chain game model with two players and product horizontal diversification is considered. Equilibrium points of the model and their stable regions are studied, and the occurrence of bifurcation is investigated by parse and simulation methods. A double route to chaos: the increase in output adjustment speeds of main chain enterprise can brake equilibrium and cause Flip fluctuation in main chain market, and can lead to market crash in epiphytic market. The increase in output adjustment speeds of epiphytic enterprise can cause Neimark–Sacker bifurcation, but has no impact on main chain enterprise. For orderly competition and stable profitability from macro-perspective, the government should pay more attention to the output adjustment speed of main chain enterprises. Finally, the nonlinear feedback method is used to control this kind of multi-product supply chain and its economic significance is presented from the standpoint of expectation theory.

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References

  1. Wang, G., Ma, J.: Modeling and complexity study of output game among multiple oligopolistic manufactures in the supply chain system. Int. J. Bifurc. Chaos 23(03), 1350038- (2013)

    Article  MATH  Google Scholar 

  2. Guo, Y., Ma, J.: Research on game model and complexity of retailer collecting and selling in closed-loop supply chain. Appl. Math. Model. 37(7), 5047–5058 (2013)

    Article  MathSciNet  Google Scholar 

  3. Sun, L., Ma, J.: Study and simulation on dynamics of a risk-averse supply chain pricing model with dual-channel and incomplete information. Int. J. Bifurc. Chaos 26(09), 1650146 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ma, J., Xie, L.: The comparison and complex analysis on dual-channel supply chain under different channel power structures and uncertain demand. Nonlinear Dyn. 83(3), 1379–1393 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ma, J., Guo, Y.: Research on third-party collecting game model with competition in closed-loop supply chain based on complex systems theory. Abstr. Appl. Anal. 2014(3), 1–22 (2014)

    MathSciNet  Google Scholar 

  6. Ma, J., Sun, L.: Complex dynamics of a MC-MS pricing model for a risk-averse supply chain with after-sale investment. Commun. Nonlinear Sci. Numer. Simul. 26(1–3), 108–122 (2015)

    Article  MathSciNet  Google Scholar 

  7. Fang, Y., Shou, B.: Managing supply uncertainty under supply chain Cournot competition. Eur. J. Oper. Res. 243(1), 156–176 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bernard, A.B., Redding, S.J., Schott, P.K.: Multiple-product firms and product switching. Am. Econ. Rev. 100(1), 70–97 (2010)

    Article  Google Scholar 

  9. Chisholm, D.C., Norman, G.: Market access and competition in product lines. Int. J. Ind. Organ. 30(5), 429–435 (2012)

    Article  Google Scholar 

  10. Garcı’A-Gallego, A., Georgantzı’S, N.: Multiproduct activity in an experimental differentiated oligopoly. Int. J. Ind. Organ. 19(3–4), 493–518 (2001)

    Article  Google Scholar 

  11. Grossmann, V.: Firm size and diversification: multiproduct firms in asymmetric oligopoly. Int. J. Ind. Organ. 25(1), 51–67 (2007)

    Article  Google Scholar 

  12. Lin, et al.: The effects of competition on the R&D portfolios of multiproduct firms. Int. J. Ind. Organ. 31(1), 83–91 (2013)

    Article  Google Scholar 

  13. Ushchev, P.: Multi-product firms in monopolistic competition: the role of scale-scope spillovers. Res. Econ. 71(4), 675–689 (2017)

    Article  Google Scholar 

  14. Ma, J., Wu, F.: The application and complexity analysis about a high-dimension discrete dynamical system based on heterogeneous triopoly game with multi-product. Nonlinear Dyn. 77(3), 781–792 (2014)

    Article  MathSciNet  Google Scholar 

  15. Wu, F., Ma, J.: The complex dynamics of a multi-product mixed duopoly model with partial privatization and cross-ownership. Nonlinear Dyn. 80(3), 1391–1401 (2015)

    Article  Google Scholar 

  16. Keshet, L.E.: Mathematical Models in Biology. Random House, New York (1992)

    MATH  Google Scholar 

  17. Salman, S.M., Yousef, A.M., Elsadany, A.A.: Stability, bifurcation analysis and chaos control of a discrete predator–prey system with square root functional response. Chaos Solitons Fractals 93, 20–31 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hu, J., Qiu, Y., Lu, H.: Adaptive robust nonlinear feedback control of chaos in PMSM system with modeling uncertainty. Appl. Math. Model. 40(19–20), 8265–8275 (2016)

    Article  MathSciNet  Google Scholar 

  19. Din, Q.: Complexity and chaos control in a discrete-time prey–predator model. Commun. Nonlinear Sci. Numer. Simul. 49, 113–134 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the reviewers for their careful reading and some pertinent suggestions. The research was supported by the National Natural Science Foundation of China (No. 71571131), the Doctoral Scientific Fund Project of the Ministry of Education of China (No. 2017M621077) and Research Plan for Science and Technology Development in Tianjin, China (No.17ZLZXZF00970).

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Authors and Affiliations

  1. School of Management, Tianjin University, Tianjin, 300072, China

    Fang Wu & Junhai Ma

  2. College of Computer and Information Engineering, Tianjin Agricultural University, Tianjin, 300384, China

    Fang Wu

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  1. Fang Wu
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  2. Junhai Ma
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Correspondence to Junhai Ma.

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Wu, F., Ma, J. The equilibrium, complexity analysis and control in epiphytic supply chain with product horizontal diversification. Nonlinear Dyn 93, 2145–2158 (2018). https://doi.org/10.1007/s11071-018-4313-z

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  • DOI: https://doi.org/10.1007/s11071-018-4313-z

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