*(English)*Zbl 1198.91164

Summary: 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.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.