scholarly journals Complexity Analysis of a Triopoly Cooperation-Competition Game Model in Convergence Product Market

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Liming Zhao ◽  
Xiaofeng Liu ◽  
Ning Ji
Keyword(s):  
Local Stability ◽  
Control Method ◽  
Complexity Analysis ◽  
Product Market ◽  
Stable Region ◽  
Price Strategy ◽  
Game Model ◽  
Feedback Control Method ◽  
Complex Relationships ◽  
Bifurcation Chaos

This work considered a tripartite cooperation-competition game model for the convergence product market, whose products are compounds of two base products or services. An early convergence product firm monopoly in this market and two potential entrants from the base products decide to cooperate with another to compete with the monopolist. We analyzed factors that affect existence and local stability of the Nash equilibrium. Rich nonlinear dynamic behaviors like bifurcation, chaos, and attractors are presented to explain the complex relationships between the three players. Results showed that the pulling effect on profit for the united R&D activity can significantly enlarge the stable region. Too frequently adjusted price strategy will bring the system into chaos. A parameter feedback control method is given to control the chaotic system and we numerically verified its effectiveness. This study has significant values to understand the fluctuations in related convergence product market.

scholarly journals Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Fang Zhang ◽  
Yanyan He
Keyword(s):  
Control Method ◽  
Complexity Analysis ◽  
Dynamic Properties ◽  
Stable Region ◽  
Largest Lyapunov Exponent ◽  
Game Model ◽  
Oligopoly Model ◽  
Long Run ◽  
Feedback Control Method ◽  
Delay Feedback Control

We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.

scholarly journals Chaos Control on a Duopoly Game with Homogeneous Strategy

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Manying Bai ◽  
Yazhou Gao
Keyword(s):  
Local Stability ◽  
Chaos Control ◽  
Control Method ◽  
Stable State ◽  
Delayed Feedback Control ◽  
Market Demand ◽  
Adaptive Expectation ◽  
Feedback Control Method ◽  
Simulation Results ◽  
Better Than

We study the dynamics of a nonlinear discrete-time duopoly game, where the players have homogenous knowledge on the market demand and decide their outputs based on adaptive expectation. The Nash equilibrium and its local stability are investigated. The numerical simulation results show that the model may exhibit chaotic phenomena. Quasiperiodicity is also found by setting the parameters at specific values. The system can be stabilized to a stable state by using delayed feedback control method. The discussion of control strategy shows that the effect of both firms taking control method is better than that of single firm taking control method.

scholarly journals Study on Triopoly Dynamic Game Model Based on Different Demand Forecast Methods in the Market

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Lijian Sun ◽  
Xueli Zhan
Keyword(s):  
Control Method ◽  
Complex Dynamics ◽  
Dynamic Game ◽  
Basins Of Attraction ◽  
Attraction Domain ◽  
Stable Region ◽  
Demand Forecast ◽  
Feedback Control Method ◽  
Set Up ◽  
The Impact

The impact of inaccurate demand beliefs on dynamics of a Triopoly game is studied. We suppose that all the players make their own estimations on possible demand with errors. A dynamic Triopoly game with such demand belief is set up. Based on this model, existence and local stable region of the equilibriums are investigated by 3D stable regions of Nash equilibrium point. The complex dynamics, such as bifurcation scenarios and route to chaos, are displayed in 2D bifurcation diagrams, in which e1 and α are negatively related to each other. Basins of attraction are investigated and we found that the attraction domain becomes smaller with the increase in price modification speed, which indicates that all the players’ output must be kept within a certain range so as to keep the system stable. Feedback control method is used to keep the system at an equilibrium state.

scholarly journals Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ting Li ◽  
Dongyun Yan ◽  
Xiaogang Ma
Keyword(s):  
Chaos Control ◽  
Stable Region ◽  
Game Model ◽  
Parameter Adaptation ◽  
Nash Equilibrium Point ◽  
Price Game ◽  
The Stability ◽  
Adaptation Method ◽  
Bifurcation Chaos

With application of nonlinear theory, this paper makes study on the long-term competition in a recycling price game model by manufacturers and retailers. The paper makes analysis on the local stability of the Nash equilibrium point and gives the corresponding stable region. It has been found that the stability of the whole system would be significantly impacted by the following factors which include adjustment speed of the recycling price, the proportion of recycled products by channels, the sensitivity of consumers for the recycling price, and the price cross-elasticity between two channels. By means of the simulation technology, the complexity of the recycling price in the system in the long-term competition has been demonstrated. Owing to the change of parameters, bifurcation, chaos, and other phenomena would appear in the system. When the system is becoming chaotic, the profit of the whole system decreased. All these show that the operational efficiency for the whole system will be impaired by the chaos. Effective chaotic control of the system will be realized by the use of the parameter adaptation method.

Vehicle Lateral Motion Control Based on Estimated Stability Regions

2017 ◽  
Author(s):  
Yiwen Huang ◽  
Yan Chen
Keyword(s):  
Measurement Errors ◽  
Local Stability ◽  
Stability Region ◽  
Control Method ◽  
Linearization Method ◽  
Stability Control ◽  
Lateral Stability ◽  
Shortest Distance ◽  
The Stability ◽  
Yaw Moment

This paper presents a novel vehicle lateral stability control method based on an estimated lateral stability region on the phase plane of vehicle yaw rate and lateral speed, which is obtained through a local linearization method. Since the estimated stability region does not only describe vehicle local stability, but also define the oversteering and understeering characteristics, the proposed control method can achieve both local stability and vehicle handling stability. Considering the irregular geometric shape of the estimated stability region, a stability analysis algorithm is designed to determine the distance between vehicle states and stability region boundaries. State estimation or measurement errors are also incorporated in the distance calculation. Based on the calculated shortest distance between vehicle states and stability boundaries, a direct yaw moment controller is designed to maintain vehicle states stay within the stability region. CarSim® and Simulink® co-simulation is applied to verify the control design through a cornering maneuver. The simulation results show that the proposed control method can make the vehicle stay within the stability region successfully and thus always operate in a safe manner.

scholarly journals Microcontroller Implementation, Chaos Control, Synchronization and Antisynchronization of Josephson Junction Model

2021 ◽  
Vol 1 (2) ◽  
pp. 198-208
Author(s):  
Rolande Tsapla Fotsa ◽  
André Rodrigue Tchamda ◽  
Alex Stephane Kemnang Tsafack ◽  
Sifeu Takougang Kingni
Keyword(s):  
Josephson Junction ◽  
Chaos Control ◽  
Control Method ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hurwitz Stability ◽  
Feedback Control Method ◽  
Different Shapes ◽  
Simulation Results

The microcontroller implementation, chaos control, synchronization, and antisynchronization of the nonlinear resistive-capacitive-inductive shunted Josephson junction (NRCISJJ) model are reported in this paper. The dynamical behavior of the NRCISJJ model is performed using phase portraits, and time series. The numerical simulation results reveal that the NRCISJJ model exhibits different shapes of hidden chaotic attractors by varying the parameters. The existence of different shapes of hidden chaotic attractors is confirmed by microcontroller results obtained from the microcontroller implementation of the NRCISJJ model. It is theoretically demonstrated that the two designed single controllers can suppress the hidden chaotic attractors found in the NRCISJJ model. Finally, the synchronization and antisynchronization of unidirectional coupled NRCISJJ models are studied by using the feedback control method.  Thanks to the Routh Hurwitz stability criterion, the controllers are designed in order to control chaos in JJ models and achieved synchronization and antisynchronization between coupled NRCISJJ models. Numerical simulations are shown to clarify and confirm the control, synchronization, and antisynchronization.

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