Nonlinear duopoly games with advertisement revisited. (English) Zbl 1215.91051
Summary: This study reconsiders a duopoly model with advertisement introduced earlier by E. Ahmed, H. N. Agiza and S. Z. Hassan [Chaos Solitons Fractals 10, No. 7, 1179–1184 (1999; Zbl 0957.91066)]. It demonstrates three major findings. The first is that the model can be destabilized via either flip bifurcation or Hopf bifurcation. The second is that a half-pitchfork bifurcation of the output occurs when the advertisement dynamics is periodic and the nonlinearity of the output dynamics becomes stronger. Finally the third is that the existence of attractor and the coexistence of attracting sets are the main features of the model when it is locally unstable.
MSC:
| 91B55 | Economic dynamics |
| 90B60 | Marketing, advertising |
| 37N40 | Dynamical systems in optimization and economics |
Citations:
Zbl 0957.91066References:
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