A Continuous Time Bertrand Duopoly Game With Fractional Delay and Conformable Derivative: Modeling, Discretization Process, Hopf Bifurcation, and Chaos - Xin, Baogui; Peng, Wei; Guerrini, Luca (Frontiers in Physics, 2019)
The purpose of this paper is threefold. First, we present a discretization process to obtain numerical solutions of a conformable fractional-order system with delays. Second, we extend the classical Bertrand duopoly game with integer delays to that with fractional delays. Third, we extend the game based on ordinary differential derivative to that based on conformable fractional-order derivative. Finally, we analyze the local stability, Hopf bifurcation, and chaos of the proposed game model.