Complex Dynamics for Airlines' Price Competition with Differentiation Strategy

To investigate the complex dynamics for airlines' price competition, this paper proposes a price competition model of airlines with differentiation strategy and with the theory of bifurcation of dynamical systems. The existence and stability of equilibrium points of the model are discussed according to dynamic stability criteria. The complex dynamics of this model in different market parameters are shown though numerical simulation. The simulation results show that the speed of price adjustment has a significant impact on the stability of the model, while the speed of price adjustment is larger than critical value, and the phenomenon of bifurcation and chaos will appear on the dynamic system. Compared with the Nash equilibrium profits, all airlines' profits are decreased obviously when chaos is occurred. Differentiation has an important impact on airlines' price and profits, it's helpful to have more competition advantage that to keep and strengthen the differentiation advantage against the competitors.