A closed-loop supply chain is a complex system in which node enterprises play important roles and exert great influence. Firstly, this paper established a collecting price game model for a close-loop supply chain system with a manufacturer and a retailer who have different rationalities. It assumed that the node enterprises took the marginal utility maximization as the basis of decision-making. Secondly, through numerical simulation, we analyzed complex dynamic phenomena such as the bifurcation, chaos and continuous power spectrum and so on. Thirdly, we analyzed the influences of the system parameters; this further explained the complex nonlinear dynamics behavior from the perspective of economics. The results have significant theoretical and practical application value.

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

Combining with the actual competition in Chinese property insurance market and assuming that the property insurance companies take the marginal utility maximization as the basis of decision-making when they play price games, we first established the price game model with three oligarchs who have different rationalities. Then, we discussed the existence and stability of equilibrium points. Third, we studied the theoretical value of Lyapunov exponent at Nash equilibrium point and its change process with the main parameters’ changes though having numerical simulation for the system such as the bifurcation, chaos attractors, and so on. Finally, we analyzed the influences which the changes of different parameters have on the profits and utilities of oligarchs and their corresponding competition advantage. Based on this, we used the variable feedback control method to control the chaos of the system and stabilized the chaos state to Nash equilibrium point again. The results have significant theoretical and practical application value.

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

This paper details the research of the Cournot– Bertrand duopoly model with the application of nonlinear dynamics theory.We analyze the stability of the fixed points by numerical simulation; from the result we found that there exists only one Nash equilibrium point. To recognize the chaotic behavior of the system, we give the bifurcation diagram and Lyapunov exponent spectrum along with the corresponding chaotic attractor. Our study finds that either the change of output modification speed or the change of price modification speed will cause the market to the chaotic state which is disadvantageous for both of the firms. The introduction of chaos control strategies can bring the market back to orderly competition.We exert control on the system with the application of the state feedback method and the parameter variation control method. The conclusion has great significance in theory innovation and practice.