Based on the work of domestic and foreign scholars and the application of chaotic systems theory, this paper presents an investigation simulation of retailer’s demand and stock. In simulation of the interaction, the behavior of the system exhibits deterministic chaos with consideration of system constraints. By the method of space’s reconstruction, the maximal Lyapunov exponent of retailer’s demand model was calculated. The result shows the model is chaotic. By the results of bifurcation diagram of model parameters k, r and changing initial condition, the system can be led to chaos.

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.

Based on Abraham C.-L. Chian’s research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements’ amplitude, frequency approximate solutions, ad system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future.

In this paper, a business cycle model with discrete delay is considered. We first investigate the stability of the equilibrium and the existence of Hopf bifurcations, and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. This research has an important theoretical value as well as practical meaning.

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.