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.

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.

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.

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.

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.