A dynamic Stackelberg duopoly model with different strategies

• The two-stage duopoly Stackelberg model is proposed.
• The local stability analysis of the equilibrium is developed.
• The dynamic of the system with different strategies has been analyzed.
• Simulations show the complex dynamics when some parameters varying.
• The model arrived at the equilibrium quickly for some controlling parameters.

In this paper, a duopoly Stackelberg model of competition on output is formulated. The firms announce plan products sequentially in planning phase and act simultaneously in production phase. For the duopoly Stackelberg model, a nonlinear dynamical system which describes the time evolution with different strategies is analyzed. We present results on existence, stability and local bifurcations of the equilibrium points. Numerical simulations demonstrate that the system with varying model parameters may drive to chaos and the loss of stability may be caused by period doubling bifurcations. It is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos.