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 MaEmail author
Original Paper


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.


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



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.


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© 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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