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Some features of application the delayed feedback controlmethod to Cournot-Puu duopoly model

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Cournot-Puu duopoly model is considered. Delayed feedback control method (DFC-method) is applied to this model. The dependence of rate coming of the system at Cournot equilibrium on the feedback coefficient K choice is shown. The optimal value of this coefficient is defined. The dependence of rate coming of the system AT Cournot equilibrium on parameter cr (the ratio of marginal cost firms) is set. The application of DFC-method with two control laws to duopoly model is considered.
Rocznik
Strony
29--37
Opis fizyczny
Bibliogr. 30 poz., rys., tab., wykr., wz.
Twórcy
autor
  • AGH University of Science and Technology, Krakow, Faculty of Management
autor
  • Lviv Polytechnic National University, Lviv, Institute of Applied Mathematics and Fundamental Sciences, Applied Mathematics Department
Bibliografia
  • 1. Agiza H.N. and Elsadany A.A. 2004. Chaotic Dynamics in nonlinear duopoly game with heterogeneous players. Applied Math, and computation, vol. 149, 843–860.
  • 2. Agiza H.N. and Elsadany A.A. 2003. Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Physica A, vol. 320, 512–524.
  • 3. Agiza H.N, Hegazi A.S. and Elsadany A.A. 2002. Complex dynamics and synchronization of duopoly game with bounded rationality. Mathematics and Computers In Simulation, vol. 58, 133–146.
  • 4. Agiza H.Z. 1999. Stability analysis and chaos control of Kopel map. Chaos, Solitons and Fractals, vol. 10, no. 11, 1909–1916.
  • 5. Agliari A., Gardini L. and Puu T. 2006a. Global bifurcation in duopoly when the Cournot point is destabilized via a subcritical Neimark bifurcation. International Game Theory Review, vol. 8, no. 1, 1–20.
  • 6. Agliari A. 2006. Homoclinic connections and subcritical Neimark bifurcations in a duopoly model with adaptively adjusted productions. Chaos, Solitons and Fractals, vol. 29, 739–755.
  • 7. Ahmed E. and Hassan S.Z. 2000. Controlling chaos Cournot games. Nonlinear Dyn. Psychol. Life Sci., vol. 4, no. 2, 189–194.
  • 8. Angelini N., Dieci R. and Nardini F. 2009. Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules. Mathematics and Computers in Simulation, vol. 79, 3179–3196.
  • 9. Bischi G.I., Chiarella C., Kopel M. and Szidarovszky F. 2009. Nonlinear Oligopolies: Stability and Bifurcations. Springer-Verlag, New York.
  • 10. Bischi G. I., Lamantia F. and Sushko I. 2012. Border collision bifurcations in a simple oligopoly model with constraints. International Journal of Applied Mathematics and Statistics, vol. 26, issue no. 2.
  • 11. Chen L. and Chen G. 2007. Controlling chaos in an economic model. Physica A, no. 374, 349-358.
  • 12. Cournot A.A. 1838. Recherches sur les principes mathematiques de la theorie des richesses. Hachette, Paris.
  • 13. Elabbasy E.M., Agiza H.N., Elsadany A.A. and ELMetwally H. 2007. The dynamics of triopoly game with heterogeneous players. International Journal of Nonlinear Science, vol. 3, no. 2, 83–90.
  • 14. Iwaszczuk N.L., Hnativ B.V. and Kavalets I.I. 2013. Pobudova uzahalnenoi modeli olihopolii Kurno-Pu ta doslidzhennia stiikosti yii tochky rivnovahy. – Kyiv. (In press).
  • 15. Iwaszczuk N. and Kavalets I. 2012. Application of mathematical models in the study of oligopolistic market / w “Zastosowania modeli matematycznych w ekonomii, finansach i bankowości”, red. P. Pusz, Rzeszow, 27-47.
  • 16. Iwaszczuk N. and Kavalets I. 2013. Delayed feedback control method for generalized Cournot-Puu oligopoly model / in “Selected Economic and Technological Aspects of Management”, ed. N. Iwaszczuk, Krakow, 108-123.
  • 17. Iwaszczuk N. and Kavalets I. 2012. Generalized Cournot-Puu oligopoly model and stability of its equilibrium point // XIV Międzynarodova Konferencji Naukowa Zarządzanie Przedsiębiorstwem – Teoria i Praktyka (22-23 listopada 2012, Krakow, Akademia Gorniczo-Hutnicza im. St. Staszica).
  • 18. Iwaszczuk N. and Kavalets I. 2013. Oligopolistic market: stability conditions of the equilibrium point of the eneralized Cournot-Puu model. – Lublin-Lviv-Cracow: Econtechmod.
  • 19. Jakimowicz A. 2012. Stability of the Cournot–Nash Equilibrium in Standard Oligopoly. Acta Physica Polonica A, vol. 121, B-50–B-53.
  • 20. Kostrobij P.P., Alekseev I.V., Thoma I.B., Hnativ B.V., Kavalets I.I. and Alekseev V.I. 2012. Matematychni modeli rehuliuvannia finansovykh potokiv. – L.: Rastr-7, 134.
  • 21. Matsumoto A. 2006. Controlling the Cournot-Nash Chaos. Journal of Optimization Theory and Applications, vol. 128, 379–392.
  • 22. Matsumoto A. and Szidarovszky F. 2011. Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games. Discrete Dynamics in Nature and Society, vol. 2011, 1–22.
  • 23. Onazaki T., Sieg G. and Yokoo M. 2003. Stability, chaos and multiple attractors: A single agent makes a difference. Journal of Economic Dynamics and Control, vol. 27, 1917–1938.
  • 24. Puu T. 1991. Chaos in duopoly pricing. Chaos, Solitons and Fractals, vol. 6, no.1, 573–581.
  • 25. Puu T. 2007. On the Stability of Cournot Equilibrium when the Number of Competitors Increases. Journal of Economic Behavior and Organization.
  • 26. Puu T. and Sushko I. (Ed.s) 2002. Oligopoly and Complex Dynamics:Models and Tools. Springer, New York.
  • 27. Rosser J.B. 2002. The development of complex oligopoly dynamics theory. In Text Book Oligopoly Dynamics:Models and Tools. Springer-Verlag.
  • 28. Sonis M. 1997. Linear Bifurcation Analysis with Applications to Relative Socio-Spatial Dynamics. Discrete Dynamics in Nature and Society, vol. 1, 45-56.
  • 29. Tramontana F. and Gardini L., Puu T. 2010. New properties of the Cournot duopoly with isoelastic dem and and constant unit costs. Working Papers Series i Economics, Mathematics and Statistics. WP-EMS, no. 1006.
  • 30. Tramontana F. 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling, vol. 27, 350–357.
Typ dokumentu
Bibliografia
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