Abstract
In the process of social development, there are a lot of competitions and confrontations. Participants in these competitions and confrontations always have different interests and goals. In order to achieve their goals, the participants must consider the opponent’s strategy to adjust their own strategies to achieve the interests of the optimization. This is called game. Based on the definition and its stability of the passive system, the passive control items are designed to the output of the duopoly competition evolution model, and the efficacy of the control methods is shown by the Lyapunov indexes. Then, the optimal function control method is taken to carry on the chaotic anticontrol to the chaotic system, and the Lyapunov indexes illustrate the control result. At last, the chaotic game of the system is introduced by combining the chaos control and anticontrol.
Highlights
In 1980, Stutzer firstly revealed the chaos phenomenon in the Haavelmo economic growth equation [1]
It has been recognized that the economic model that is based on the traditional economic theory has inherent randomness, which makes the effects of intervention means taken by traditional ways such as the fiscal policy or the financial policy and other corresponding macrocontrol means very limited [2]
Because the economic system has the dissipative structure property, in this paper, we introduce the passive control method in Section 5 to conduct the chaos control to the model; the global stability of the system is achieved by constructing passive control item based on passive theory, and the effectiveness of the results can be showed by numerical simulation
Summary
In 1980, Stutzer firstly revealed the chaos phenomenon in the Haavelmo economic growth equation [1]. Because the economic system has the dissipative structure property, in this paper, we introduce the passive control method in Section 5 to conduct the chaos control to the model; the global stability of the system is achieved by constructing passive control item based on passive theory, and the effectiveness of the results can be showed by numerical simulation. Considering that the static game can not respond in a timely manner, the emergence of differential game solves this problem; that is, one first makes the decision and the other determines the output according to the previous decision information and the current decision, making decision-making more effective In this paper, this idea is applied to the chaotic game of the output duopoly competing evolution model in Sections 3 and 7.
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