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 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 Bionic Control of Cheetah Bounding with a Segmented Spine

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Chunlei Wang ◽  
Shigang Wang
Keyword(s):  
Control Method ◽  
Dynamic Properties ◽  
Biological Properties ◽  
The Body ◽  
Body Balance ◽  
Feedback Control Method ◽  
Dimensional Parameters ◽  
Delay Feedback Control ◽  
The Stability ◽  
Bounding Gait

A cheetah model is built to mimic real cheetah and its mechanical and dimensional parameters are derived from the real cheetah. In particular, two joints in spine and four joints in a leg are used to realize the motion of segmented spine and segmented legs which are the key properties of the cheetah bounding. For actuating and stabilizing the bounding gait of cheetah, we present a bioinspired controller based on the state-machine. The controller mainly mimics the function of the cerebellum to plan the locomotion and keep the body balance. The haptic sensor and proprioception system are used to detect the trigger of the phase transition. Besides, the vestibular modulation could perceive the pitching angle of the trunk. At last, the cerebellum acts as the CPU to operate the information from the biological sensors. In addition, the calculated results are transmitted to the low-level controller to actuate and stabilize the cheetah bounding. Moreover, the delay feedback control method is employed to plan the motion of the leg joints to stabilize the pitching motion of trunk with the stability criterion. Finally, the cyclic cheetah bounding with biological properties is realized. Meanwhile, the stability and dynamic properties of the cheetah bounding gait are analyzed elaborately.

scholarly journals Complexity of a Duopoly Game in the Electricity Market with Delayed Bounded Rationality

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Hongliang Tu
Keyword(s):  
Nash Equilibrium ◽  
Bounded Rationality ◽  
Electricity Market ◽  
Complex Dynamics ◽  
Fractal Dimensions ◽  
Practical Significance ◽  
Stable Region ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Game Model

According to a triopoly game model in the electricity market with bounded rational players, a new Cournot duopoly game model with delayed bounded rationality is established. The model is closer to the reality of the electricity market and worth spreading in oligopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Its complex dynamics is demonstrated by means of the largest Lyapunov exponent, bifurcation diagrams, phase portraits, and fractal dimensions. Since the output adjustment speed parameters are varied, the stability of Nash equilibrium gives rise to complex dynamics such as cycles of higher order and chaos. Furthermore, by using the straight-line stabilization method, the chaos can be eliminated. This paper has an important theoretical and practical significance to the electricity market under the background of developing new energy.

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 Vertical Vibration Control of Cold Rolling Mill’s Rolls Based on Time-delay Feedback Control Method

2018 ◽  
Vol 153 ◽  
pp. 06005
Author(s):  
Dongxiao Hou
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Cold Rolling ◽  
Rolling Mill ◽  
Control Method ◽  
Primary Resonance ◽  
Vertical Vibration ◽  
Resonance Amplitude ◽  
Feedback Control Method ◽  
Delay Feedback Control

In this paper, a two degree of freedom nonlinear vertical vibration equation of the cold rolling mill with the dynamic rolling force was established, then the delay feedback control method was introduced into the equation to controlled the vertical vibration of the system. The amplitude-frequency equations of primary resonance of system was carried out by using the multi-scale method, and the resonance characteristics of different parameters of delay feedback control method were obtained by adopting the actual parameters of rolling mill. It is found that the size of the resonance amplitude value was effectively controlled and the resonance region and jumping phenomenon of the system were eliminated by selecting the appropriate time-delay parameters combination, which provides an effective theoretical reference for solving mill vibration problems.

Car-following model based delay feedback control method with the gyroidal road

2019 ◽  
Vol 30 (09) ◽  
pp. 1950073 ◽  
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Feedback Control ◽  
Traffic Flow ◽  
Delay Time ◽  
Control Method ◽  
Gain Coefficient ◽  
Car Following ◽  
Controller Gain ◽  
Car Following Model ◽  
Feedback Control Method ◽  
Delay Feedback Control

Connected vehicles are expected to become commercially available by the next decade. In this work, we propose a delay feedback control method for car-following model on a gyroidal road. By using the Hurwitz criteria and the condition for transfer function in terms of [Formula: see text]-norm, the impact of controller gain coefficient and the delay time on the performance of traffic flow is investigated. Based on the bode curve, we verify that the designed delay feedback controller is effective in suppressing traffic congestion and reducing energy consumption. The enhanced traffic flow model is more sensitive to the controller gain coefficient and delay time at downhill situation compared to the uphill situation. The conclusion obtained from the simulation example is consistent with the theoretical analysis.

scholarly journals Complex Dynamics Analysis for a Cournot-Bertrand Mixed Game Model with Delayed Bounded Rationality

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Junhai Ma ◽  
Hongwu Wang
Keyword(s):  
Mixed Model ◽  
Historical Data ◽  
Complex Dynamics ◽  
Dynamic Properties ◽  
Stable Region ◽  
Mixed Duopoly ◽  
Game Model ◽  
Complex Dynamic ◽  
Delayed System ◽  
Route To Chaos

A Cournot-Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot-Bertrand mixed model is considered and the results show that the delayed system has the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability.

scholarly journals On a New Cournot Duopoly Game

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
H. N. Agiza ◽  
A. A. Elsadany ◽  
M. M. El-Dessoky
Keyword(s):  
Nash Equilibrium ◽  
Control Method ◽  
Chaotic Behavior ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Feedback Control Method ◽  
Delay Feedback Control ◽  
Stability And Bifurcations ◽  
Theoretical Results

This paper presents a new Cournot duopoly game. The main advantage of this game is that the outputs are nonnegative for all times. We investigate the complexity of the corresponding dynamical behaviors of the game such as stability and bifurcations. Computer simulations will be used to confirm our theoretical results. It is found that the chaotic behavior of the game has been stabilized on the Nash equilibrium point by using delay feedback control method.

scholarly journals Delay Feedback Control of the Lorenz-Like System

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Qin Chen ◽  
Jianguo Gao
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Method ◽  
Functional Differential Equations ◽  
Variable Parameter ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Feedback Control Method ◽  
Delay Feedback Control

We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.

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