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Nonlinear Dynamics

, Volume 93, Issue 4, pp 2145–2158 | Cite as

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

  • Fang Wu
  • Junhai Ma
Original Paper

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.

Keywords

Multi-product Epiphytic Flip Neimark–Sacker Supply chain Complexity Chaos 

Notes

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).

Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflict of interest to this work.

References

  1. 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)CrossRefzbMATHGoogle Scholar
  2. 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)MathSciNetCrossRefGoogle Scholar
  3. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 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)MathSciNetGoogle Scholar
  6. 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)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fang, Y., Shou, B.: Managing supply uncertainty under supply chain Cournot competition. Eur. J. Oper. Res. 243(1), 156–176 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bernard, A.B., Redding, S.J., Schott, P.K.: Multiple-product firms and product switching. Am. Econ. Rev. 100(1), 70–97 (2010)CrossRefGoogle Scholar
  9. 9.
    Chisholm, D.C., Norman, G.: Market access and competition in product lines. Int. J. Ind. Organ. 30(5), 429–435 (2012)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 11.
    Grossmann, V.: Firm size and diversification: multiproduct firms in asymmetric oligopoly. Int. J. Ind. Organ. 25(1), 51–67 (2007)CrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 13.
    Ushchev, P.: Multi-product firms in monopolistic competition: the role of scale-scope spillovers. Res. Econ. 71(4), 675–689 (2017)CrossRefGoogle Scholar
  14. 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)MathSciNetCrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 16.
    Keshet, L.E.: Mathematical Models in Biology. Random House, New York (1992)zbMATHGoogle Scholar
  17. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 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)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Din, Q.: Complexity and chaos control in a discrete-time prey–predator model. Commun. Nonlinear Sci. Numer. Simul. 49, 113–134 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ManagementTianjin UniversityTianjinChina
  2. 2.College of Computer and Information EngineeringTianjin Agricultural UniversityTianjinChina

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