TY - JOUR
T1 - On the Dynamics of a Discrete Fractional-Order Cournot-Bertrand Competition Duopoly Game
AU - Al-Khedhairi, Abdulrahman
AU - Elsadany, Abdelalim A.
AU - Elsonbaty, Amr
N1 - Publisher Copyright:
© 2022 Abdulrahman Al-Khedhairi et al.
PY - 2022
Y1 - 2022
N2 - A discreet fractional-order Cournot-Bertrand competition duopoly game is introduced based on the fractional-order difference calculus of the Caputo operator. The model is designed when players can make long memory decisions. The local stability of equilibrium points is discussed for the proposed model. Some numerical simulations explore the model's bifurcation and chaos by employing bifurcation diagrams, phase portraits, maximal Lyapunov exponents, and time series. According to our findings, the fractional-order parameter has an effect on the game's stability and dynamics.
AB - A discreet fractional-order Cournot-Bertrand competition duopoly game is introduced based on the fractional-order difference calculus of the Caputo operator. The model is designed when players can make long memory decisions. The local stability of equilibrium points is discussed for the proposed model. Some numerical simulations explore the model's bifurcation and chaos by employing bifurcation diagrams, phase portraits, maximal Lyapunov exponents, and time series. According to our findings, the fractional-order parameter has an effect on the game's stability and dynamics.
UR - http://www.scopus.com/inward/record.url?scp=85125425164&partnerID=8YFLogxK
U2 - 10.1155/2022/8249215
DO - 10.1155/2022/8249215
M3 - Article
AN - SCOPUS:85125425164
SN - 1024-123X
VL - 2022
JO - Mathematical Problems in Engineering
JF - Mathematical Problems in Engineering
M1 - 8249215
ER -