On the dynamics of a nonlinear reaction–diffusion duopoly model. (March 2018) - Rionero, Salvatore; Torcicollo, Isabella
Abstract: The self and cross diffusion action on the dynamic of the nonlinear continuous duopoly model introduced in Torcicollo (2016), is investigated. Under Robin boundary conditions the longtime behavior and the linear and nonlinear stability of the steady states, are studied. The self and cross diffusion parameters guaranteeing the spreading of the firms outputs, are characterized. Highlights: A generalization of the duopoly model introduced in [1], via a PDEs system is considered. The diffusion action on the dynamic of the model introduced is investigated. The linear stability analysis of the critical points of the system is investigated. The nonlinear asymptotic stability of equilibrium of conjectural variation is obtained.