| Citation: |
Haibo Luo, Weihua Sun. CONTROL OF JULIA SETS OF COURNOT-BERTRAND DUOPOLY GAME MODEL[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2427-2439. doi: 10.11948/20240489
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CONTROL OF JULIA SETS OF COURNOT-BERTRAND DUOPOLY GAME MODEL
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Abstract
Cournot-Bertrand duopoly game model is a very important model in the economic field. Based on the idea of feedback control, three controllers are designed to control Julia sets of Cournot-Bertrand duopoly game model in this study. The first method is the feedback control by use of the fixed point, the second is based on feedback control and cumulative error and the third is designed based on the feedback control and difference. The efficacy of three control methods is illustrated in simulations.
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Keywords:
- Julia set /
- feedback control /
- Cournot-Bertrand duopoly game model
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References
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Haibo Luo, Weihua Sun. CONTROL OF JULIA SETS OF COURNOT-BERTRAND DUOPOLY GAME MODEL[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 2427-2439. doi: 10.11948/20240489
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Figure 1.
Julia sets for model (2.1) when
$ \alpha= 2.05 $ $ \beta=0.2 $ $ c=2.7 $ $ d= 0.8 $ -
Figure 2.
Estimation of the distribution range of values of k that stabilize the fixed point.
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Figure 3.
Variation of Julia sets of the controlled system (3.3) with control parameter k.
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Figure 4.
Estimation of the distribution range of values of k that make the fixed point
$ (q^*,p^*,0,0) $ -
Figure 5.
Variation of Julia sets of the controlled system (3.5) with control parameter k.
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Figure 6.
Estimation of the distribution range of values of k that make the fixed point be stable.
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Figure 7.
Variation of Julia sets of the controlled system (3.8) with control parameter k.