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 Complexity Analysis of a Cournot-Bertrand Duopoly Game Model with Limited Information

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongwu Wang ◽  
Junhai Ma
Keyword(s):  
Complex Dynamics ◽  
Complexity Analysis ◽  
Mixed Duopoly ◽  
Decision Variable ◽  
Game Model ◽  
Limited Information ◽  
Nash Equilibrium Point ◽  
Route To Chaos ◽  
The One ◽  
Degree Of Differentiation

A Cournot-Bertrand mixed duopoly game model with limited information about the market and opponent is considered, where the market has linear demand and two firms have the same fixed marginal cost. The principles of decision-making are bounded rational. One firm chooses output and the other chooses price as decision variable, with the assumption that there is a certain degree of differentiation between the products offered by firms to avoid the whole market being occupied by the one that applies a lower price. The existence of Nash equilibrium point and its local stability of the game are investigated. The complex dynamics, such as bifurcation scenarios and route to chaos, are displayed using parameter basin plots by numerical experiment. The influences of the parameters on the system performance are discussed from the perspective of economics.

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 Research on the Complex Dynamic Characteristics and RLS Estimation’s Influence Based on Price and Service Game

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Zhanbing Guo
Keyword(s):  
Least Squares ◽  
Fixed Points ◽  
Dynamic Characteristics ◽  
Complex Dynamics ◽  
Recursive Least Squares ◽  
Game Model ◽  
Complex Dynamic ◽  
Service Market ◽  
The Real ◽  
Price Game

Considering that the real competitions in service market contain two important factors, price and service, we build a dynamical price and service game model and study the complex dynamics of this bivariate game. Some special properties about the adjustment of service are noted by comparing our innovative bivariate game model with previous univariate game model. Besides, we discuss the stabilities of fixed points and compare the price and service game with price game. What is more, the recursive least-squares (RLS) estimation is introduced to substitute naive estimation; then the impacts of RLS estimation are studied by comparing it with naive estimation.

scholarly journals Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

2021 ◽  
pp. 47-57
Author(s):  
Yuqi Dou ◽  
Xingyu Liu
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Systems ◽  
Complex Dynamics ◽  
Rational Expectation ◽  
Profit Maximization ◽  
Mixed Duopoly ◽  
Complex Dynamic ◽  
Discrete Dynamic Systems ◽  
The Stability ◽  
Relative Profit

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

Theory of chaos synchronization and quasi-period synchronization of an all optic 2n-D LAN

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yan Senlin
Keyword(s):  
Chaos Synchronization ◽  
Local Area Network ◽  
Local Area ◽  
Double Star ◽  
Stable Region ◽  
Area Network ◽  
Complex Dynamic ◽  
Network Nodes ◽  
Coupled Lasers ◽  
Route To Chaos

Abstract Theory of chaos synchronization and quasi-period synchronization of an all optics local area network (O-LAN) is deeply studied and discussed, where two coupled-lasers are used as network’s double-star and the other single-lasers are used as network nodes. The LAN operates double-star lasers to drive node lasers in two links to perform a 2n−D (n is a positive integer, dimensions (D)) laser network. The O-LAN has the characteristics of an all optics LAN with double-center and two link nodes. Our theoretical and numerical results prove that the double-center lasers can obtain their synchronizations with each laser in two link nodes. A route to chaos after a quasi-period bifurcation is analyzed to illustrate dynamics distribution region of O-LAN. We find five quasi-period regions, four chaos regions, where there is a region where instability mixes with the first chaos, and a stable region. We find also that O-LAN can obtain its parallel multi-dynamics synchronizations, such as cycle-one synchronization, cycle-2 synchronization, cycle-3 synchronization, cycle-4 synchronization, cycle-5 synchronization, other quasi-period synchronization and chaos synchronization, shown in two links of O-LAN by shifting the currents of the lasers in one link. The theory of all optics LAN and its obtained results are useful to study on complex dynamic system, optics network, artificial intelligence, chaos and its synchronization.

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 Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Hongliang Tu ◽  
Xueli Zhan ◽  
Xiaobing Mao
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Complex Dynamics ◽  
Spillover Effects ◽  
Game Model ◽  
Complex Dynamic ◽  
Nash Equilibrium Point ◽  
Straight Line ◽  
Stable Conditions ◽  
The Stability

We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos.

scholarly journals Portrayal of Complex Dynamic Properties of Sugarcane Defensin 5 by NMR: Multiple Motions Associated with Membrane Interaction

Structure ◽  
2011 ◽  
Vol 19 (1) ◽  
pp. 26-36 ◽  
Author(s):  
Viviane Silva de Paula ◽  
Guilherme Razzera ◽  
Eliana Barreto-Bergter ◽  
Fabio C.L. Almeida ◽  
Ana Paula Valente
Keyword(s):  
Dynamic Properties ◽  
Complex Dynamic ◽  
Membrane Interaction

The Effect of Compositional and Testing Variations on the Dynamic Properties of Compounds Based on Styrene-Butadiene and Polybutadiene Elastomers

1971 ◽  
Vol 44 (1) ◽  
pp. 258-270 ◽  
Author(s):  
D. A. Meyer ◽  
J. G. Sommer
Keyword(s):  
Carbon Black ◽  
Storage Modulus ◽  
Dynamic Properties ◽  
Loss Modulus ◽  
Dynamic Stiffness ◽  
Rate Of Change ◽  
Complex Dynamic ◽  
Spring Rate ◽  
Styrene Butadiene ◽  
Black Level

Abstract Important factors of potential use for manipulating static and dynamic stiffness and the damping characteristics of compounds based on styrene-butadiene and polybutadiene elastomers and their blends have been outlined. Their characteristics have been compared with those of IIR and EPDM compounds. The effects of variations in composition are quantitatively defined to assist the compounder in combining these effects in a manner that will lead to a desired combination of properties. In addition to the expected increase in static spring rate and dynamic spring rate with carbon black level, the following responses to compositional variations were found important: 1. The complex dynamic spring rate is more sharply dependent upon carbon black level than the static spring rate. 2. The complex dynamic spring rate is essentially independent of the level of crosslinking while static spring rate increases. 3. Damping coefficient is directly proportional to the level of carbon black and inversely proportional to the level of crosslinking. 4. Styrene level in a polymer blend and plasticizer composition can be used to adjust loss modulus and storage modulus at a given temperature and also to modify the rate of change of these properties with temperature. 5. The strain dependency of storage modulus was found in one instance to vary with the elastomer composition. The IIR vulcanizate, when formulated to the same static modulus, exhibited a larger strain dependence than the SBR, BR, and EPDM composition.

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