A dynamic duopoly model with bounded rationality based on constant conjectural variation

- We construct dynamic models on the basis of constant conjectural variation.
- We consider constructing a dynamic system of duopolists with bounded rationality.
- The complexion of dynamic models is analyzed by numerical simulation.
- Bifurcation and chaos occur with the speed of output adjustment increasing.
- Strange attractors and fractal dimensions are also shown in this article.

In this paper, we construct dynamic models on the basis of constant conjectural variation. Duopolists with dynamic adjustment behavior of bounded rationality have been considered. Numerical simulation is used to illustrate the complexion of models. The existence of equilibrium points and their stability in this nonlinear system are discussed. We study two special cases of symmetry model and Bertrand model with conjectural variation. When the speed of output adjustment changes, a series of complex phenomena including bifurcation, chaos and strange attractors can be observed in our models. We also analyzed the importance of the initial conditions to the system that a tiny variation of the initial value will cause dramatic fluctuations in output.