Chaos Control and Anticontrol of the Output Duopoly Competing Evolution Model

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.

The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players

“…Due to the complex dynamics and inherent instability of the chaotic models, controlling them so that they exhibit the desired behavior seems impossible. However, it has been shown in various references that chaotic duopoly models are controllable, and different control goals can be imagined for them [47][48][49]. Since it has been shown that the proposed model can put forward complex, chaotic behaviors, and this model is a sample of a market, unpredictable behaviors are unsuitable for the firms working in this market.…”

Research on a New Singularity-Free Controller for Uncertain Lorenz System

“…Generally speaking, any monotonically increasing odd activation function ϕ(•) could be used for the construction of the dynamics model. In this paper, we choose the linear activation function ϕ(e) = e. Remark 1 [29]: If the linear activation function ϕ(•) is used, the exponential convergence with rate γ could be achieved for ZD model (7). In addition, if the power-sigmoid activation function is used, superior convergence can be achieved over the whole error range (−∞, +∞), as compared to the linear case.…”