AUTHOR=Xin Baogui , Peng Wei , Guerrini Luca TITLE=A Continuous Time Bertrand Duopoly Game With Fractional Delay and Conformable Derivative: Modeling, Discretization Process, Hopf Bifurcation, and Chaos JOURNAL=Frontiers in Physics VOLUME=7 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00084 DOI=10.3389/fphy.2019.00084 ISSN=2296-424X ABSTRACT=

The purpose of this paper is three-fold. 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.