Nonlinear analysis and chaos control of the complex dynamics of multi-market Cournot game with bounded rationality

2019 ◽  
Vol 162 ◽  
pp. 45-57 ◽  
Author(s):  
LiuWei Zhao ◽  
Jianguo Du ◽  
QiWei Wang
Keyword(s):  
Nonlinear Analysis ◽  
Bounded Rationality ◽  
Chaos Control ◽  
Complex Dynamics ◽  
Cournot Game

scholarly journals Nonlinear Complex Dynamics of Carbon Emission Reduction Cournot Game with Bounded Rationality

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
LiuWei Zhao
Keyword(s):  
Bounded Rationality ◽  
Emission Reduction ◽  
Carbon Emission ◽  
Complex Dynamics ◽  
Dynamic Properties ◽  
Dynamic Adjustment ◽  
Carbon Emission Reduction ◽  
Cournot Game ◽  
Existence And Stability ◽  
The Stability

Based on the hypothesis of participant’s bounded rationality, our study formulated a novel Cournot duopoly game model of carbon emission reduction and, subsequently, analyzed the dynamic adjustment mechanism of emission reduction for enterprises. The existence and stability of the equilibrium solution of game are further discussed by the nonlinear dynamics theory. Our findings revealed that the parameters have key significance on the dynamic properties of the system. However, when the adjustment speed gets too large, the system loses the original stability and vividly demonstrates complex chaos phenomenon. Higher market prices in carbon trading have an outstanding impact on the stability of the system, which easily leads to system instability. Our study further controlled the chaos behavior of the power system by the delay feedback control. The results of the numerical analysis depict that the unstable behavior of the dynamic system can be controlled efficiently and quickly, in the quest to restore back a stable and orderly market. Our novel method is proved to have provided decision makers with effective solution to market instability.

Bifurcations and chaos control in a discrete-time biological model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050022 ◽  
Author(s):  
A. Q. Khan ◽  
T. Khalique
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Complex Dynamics ◽  
Small Neighborhood ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Time Model ◽  
Predator Prey Model

In this paper, bifurcations and chaos control in a discrete-time Lotka–Volterra predator–prey model have been studied in quadrant-[Formula: see text]. It is shown that for all parametric values, model has boundary equilibria: [Formula: see text], and the unique positive equilibrium point: [Formula: see text] if [Formula: see text]. By Linearization method, we explored the local dynamics along with different topological classifications about equilibria. We also explored the boundedness of positive solution, global dynamics, and existence of prime-period and periodic points of the model. It is explored that flip bifurcation occurs about boundary equilibria: [Formula: see text], and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of [Formula: see text]. Further, it is also explored that about [Formula: see text] the model undergoes a N–S bifurcation, and meanwhile a stable close invariant curves appears. From the perspective of biology, these curves imply that between predator and prey populations, there exist periodic or quasi-periodic oscillations. Some simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and 23. The Maximum Lyapunov exponents as well as fractal dimension are computed numerically to justify the chaotic behaviors in the model. Finally, feedback control method is applied to stabilize chaos existing in the model.

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.

Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders

1995 ◽  
Vol 51 (1) ◽  
pp. 102-110 ◽  
Author(s):  
Weiming Yang ◽  
Mingzhou Ding ◽  
Arnold J. Mandell ◽  
Edward Ott
Keyword(s):  
Chaos Control ◽  
Complex Dynamics ◽  
Control Strategies

scholarly journals Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Askar ◽  
Mona F. EL-Wakeel ◽  
M. A. Alrodaini
Keyword(s):  
Utility Function ◽  
Complex Dynamics ◽  
Discrete Dynamical System ◽  
Cournot Oligopoly ◽  
Differentiated Products ◽  
Time Step ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
3 Dimensional ◽  
Cournot Game

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm’s preference is represented by a utility function that is derived from a constant elasticity of substitution (CES) production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations.

scholarly journals On a Cournot Game with Bounded Rational Players, Convex, Log-Linear Demand and Consumer Surplus

2020 ◽  
Author(s):  
Georges Sarafopoulos ◽  
Kosmas Papadopoulos
Keyword(s):  
Dynamical System ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Discrete Dynamical System ◽  
Consumer Surplus ◽  
Cournot Oligopoly ◽  
Cournot Game ◽  
Linear Demand ◽  
Log Linear

Based on the Cournot oligopoly game and the nonlinear dynamics theory, we study the behavior of semi-public enterprises by considering corporate social responsibility into their objectives. The model that is established is a dynamical Cournot-type duopoly model with bounded rationality containing the consumer surplus. We suppose quadratic cost function and a convex, log-linear demand function. The game is modeled with a system of two difference equations. Existence and stability of equilibriums of this system are studied. More complex chaotic and unpredictable trajectories are resulted studying this discrete dynamical system. The complex dynamics of the system are demonstrated numerically via computing Lyapunov numbers, sensitivity dependence on initial conditions, and bifurcation diagrams. Keywords: Cournot duopoly game; Discrete dynamical system; Homogeneous expectations; Stability; Chaotic Behavior; Consumer Surplus.

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