Abstract__At first, the paper described a brief history of communication in China. In 2008,
the third generation (3G) telecommunication technologies began to develop. In Chinese
3G telecommunication market, there are three oligopolistic competitors. In order to study
competing process of the triopoly, the paper considered a Bertrand model with bounded
rational. A triopoly game is modeled by three nonlinear difference equations. By using the
theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this
system were obtained. Numerical simulations were used to show bifurcations diagrams,
the maximum Lyapunov exponent and sensitive dependence on initial conditions. We
observed that increasing the speed of adjustment of bounded rational player might change
the stability of Nash equilibrium point and cause bifurcation and chaos to occur. Thus, it
will be difficult to make strategy and to forecast for each enterprise. It might cause the telecom
markets to be irregular. The analysis and results in this paper are important for Chinese
telecommunication markets, the same to mathematics.