According to the repeated game model in electric power duopoly, a triopoly outputs game model is presented. On the basis of some hypotheses, the dynamic characters are demonstrated with theoretical analysis and numerical simulations. The results show that the triopoly model is a chaotic system and it is better than the duopoly model in applications.

A triopoly price game model has been established based on nonlinear and economics theories in this paper, and all 3 firms of triopoly market are supposed to make a price decision with bounded rationality. By discrete dynamical system theory and jury condition, we obtain the expression of Nash equilibrium point’s stable region. Then traditional twodimensional and creative three-dimensional diagrams of the local stable region are given by numerical simulation, and both 2D and 3D diagrams showed us some law about the Nash equilibrium point’s stable region. First, the number of time-delay decision makers has no necessary relationship with system stability; Second, under the same number of time-delay decision makers, the delay parameter has a positive influence of system stability, i.e., the price making relying more on current period profits can lower the system risk of falling into chaos. These results have significant theoretical and practical value to the price making of firms in related markets

We establish a nonlinear real estate model based on cobweb theory, where the demand function and supply function are quadratic. The stability conditions of the equilibrium are discussed.We demonstrate that as some parameters varied, the stability of Nash equilibrium is lost through period-doubling bifurcation. The chaotic features are justified numerically via computing maximal Lyapunov exponents and sensitive dependence on initial conditions. The delayed feedback control (DFC) method is applied to control the chaos of system.

A Cournot-Bertrand mixed duopoly game model is constructed.The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot-Bertrand mixed model is considered and the results show that the delayed systemhas the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability

Based on the researches of Szydlowski and Krawiec, we studied the inherent complexity of a chaotic business cycle with great excitements in non-resonant condition. First, we got the first-order and second-order pproximate solutions of the system by using multiple scale method. Then deduced the formulation reflecting the complex relations between vibration, phase, bifurcation parameter l and excite frequency X of first-order solution. As the great excitement F varied, the global changes of the system solutions were analyzed. We also explored the different paths leading the systems with different parameter combinations into catastrophe region, fuzzy region or chaos region. Finally, we discussed the evolution trends of business cycle models under the above-mentioned conditions. Hence, this paper has some theoretical and practical significance.