Analysis of a Cournot-Bertrand Duoploy Game with Differentiated Products: Stability, Bifurcation and Control

this work, we investigate a Cournot-Bertrand duopoly model with product differentiation between two different firms, where one company uses price as decision variable and the other quantity. The stability of Nash equilibrium point is investigated, role parameters on studied. It shown that system experiences three types bifurcations when go through boundary curves region. Furthermore, model's bifurcation controlled using hybrid control strategy.