Nonlinear Dynamics

, Volume 74, Issue 1–2, pp 45–54 | Cite as

The complex dynamics of R&D competition models of three oligarchs with heterogeneous players

  • Ting Li
  • Junhai Ma
Original Paper


This paper uses the theory of bifurcations of dynamical systems, considering R&D input competition model in oligopoly market with heterogeneous rationality. We assume that cooperation, as well as competition, exists among the oligarchs, which are closer to reality and different from previous studies. On the basis of analyzing the stabilities of four fixed points in the three-dimensional dynamic system, a local stable region of Nash equilibrium is obtained. Simulation results show that the adjustment of R&D input speed has an obvious impact on the complexity of competition, and also show that the system profit will decrease when it is in chaos. So this paper discusses the application of parameters control method when the model is in chaos and then allows the oligarchs to eliminate the negative effects.


Triopoly R&D competition Heterogeneous rationality Chaos control 



This work was supported by the National Nature Science Foundation of China (No. 61273231) and the Doctoral Scientific Fund Project of the Ministry of Education of China (No. 20090032110031).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of Management and EconomicsTianjin UniversityTianjinChina
  2. 2.School of Economics and ManagementDezhou UniversityDezhouChina

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