scholarly journals Analysis and Control of the Complex Dynamics of a Multimarket Cournot Investment Game with Bounded Rationality

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
LiuWei Zhao
Keyword(s):  
Demand Function ◽  
Complex Dynamics ◽  
Delayed Feedback Control ◽  
Flip Bifurcation ◽  
Bifurcation And Chaos ◽  
Stability And Instability ◽  
The Stability ◽  
And Control ◽  
Time Delayed Feedback ◽  
Dynamic Phenomena

A dynamic multimarket Cournot model is introduced based on a specific inverse demand function. Puu’s incomplete information approach, as a realistic method, is used to contract the corresponding dynamical model under this function. Therefore, some stability analysis is carried out on the model to detect the stability and instability conditions of the system’s Nash equilibrium. Based on the analysis, some dynamic phenomena such as bifurcation and chaos are found. Numerical simulations are used to provide experimental evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium of the system can lose stability via flip bifurcation or Neimark-Sacker bifurcation and time-delayed feedback control is used to stabilize the chaotic behaviors of the system.

Simulation and Control of a Duopoly Model

2014 ◽  
Vol 472 ◽  
pp. 146-151
Author(s):  
Ya Li Lu
Keyword(s):  
Nash Equilibrium ◽  
Demand Function ◽  
Delayed Feedback Control ◽  
Control Scheme ◽  
Duopoly Model ◽  
Adjustment Speed ◽  
The Stability ◽  
Boundary Fixed Points ◽  
And Control ◽  
Time Delayed Feedback

This paper studies the dynamics of a duopoly model with bounded rationality and nonlinear demand function. Based on the stability theorem and Jurys criterions, we prove that the model has two unstable boundary fixed points and a local stable Nash equilibrium. Then we depict the stability region of Nash equilibrium, and investigate the effects of output adjustment speed on the players profit respectively. Theoretical analysis and simulations show that higher output adjustment speed can result in chaotic variation of outputs, and that the Nash equilibrium is the optimal result of duopoly game. To improve the profitability of each player and achieve the optimal game result, we put forth a new scheme combined with the time-delayed feedback control and the limiter control to stabilize the output to Nash equilibrium. Finally, the numerical simulation is adopted to verify the effectiveness and feasibility of the above control scheme.

scholarly journals Complexity Analysis of Dynamic Cooperative Game Models for Supply Chain with the Remanufactured Products

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Jianwei Chang ◽  
Liuwei Zhao
Keyword(s):  
Supply Chain ◽  
Complexity Analysis ◽  
Stackelberg Game ◽  
Delayed Feedback Control ◽  
Flip Bifurcation ◽  
Maximum Lyapunov Exponent ◽  
Bifurcation And Chaos ◽  
Coupling Dynamics ◽  
Time Delayed Feedback ◽  
Dynamic Phenomena

This study focused on the supply chain within the remanufacturing production system, which is composed of one manufacturer and one retailer. In this case, the manufacturer is responsible for the production of new products and the remanufactured products. This system can be regarded as a coupling dynamics of the forward supply chain of Stackelberg game model. Based on the analysis, some dynamic phenomena such as bifurcation and chaos were found. Numerical simulations and the maximum Lyapunov exponent were therefore utilized to provide experimental evidence for the complicated behaviors of the system evolution. The findings of the study revealed that the equilibrium of the system can lose stability via flip bifurcation or Neimark-Sacker bifurcation and that time-delayed feedback control is appropriate for stabilizing the chaotic behaviors of the system.

scholarly journals Complex dynamics and control investigation of a Cournot triopoly game formed based on a log-concave demand function

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401770281 ◽  
Author(s):  
K Alnowibet ◽  
SS Askar ◽  
AA Elsadany
Keyword(s):  
Local Stability ◽  
Demand Function ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Phase Portraits ◽  
Control Scheme ◽  
Sensitive Dependence ◽  
Dynamics And Control ◽  
The Stability ◽  
And Control

This article investigates the dynamics of a Cournot triopoly game whose demand function is characterized by log-concavity. The game is formed using the bounded rationality approach. The existence and local stability of steady states of the game are analyzed. We find that an increase in the game parameters out of the stability region destabilizes the Cournot–Nash steady state. We confirm our obtained results using some numerical simulation. The simulation shows the consistence with the theoretical analysis and displays new and interesting dynamic behaviors, including bifurcation diagrams, phase portraits, maximal Lyapunov exponent, and sensitive dependence on initial conditions. Finally, a feedback control scheme is adopted to overcome the uncontrollable behavior of the game’s system occurred due to chaos.

scholarly journals Complex Dynamics in a Nonlinear Cobweb Model for Real Estate Market

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Junhai Ma ◽  
Lingling Mu
Keyword(s):  
Real Estate ◽  
Demand Function ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Period Doubling ◽  
Real Estate Market ◽  
Delayed Feedback Control ◽  
Cobweb Model ◽  
Sensitive Dependence ◽  
The Stability

We establish a nonlinear real estate model based on cobweb theory, where the demand function and supply function are quadratic. The stability conditions of the equilibrium are discussed. We demonstrate that as some parameters varied, the stability of Nash equilibrium is lost through period-doubling bifurcation. The chaotic features are justified numerically via computing maximal Lyapunov exponents and sensitive dependence on initial conditions. The delayed feedback control (DFC) method is applied to control the chaos of system.

scholarly journals Dynamics of a Duopoly Game with Two Different Delay Structures

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Shumin Jiang ◽  
Fei Xu ◽  
Zhanwen Ding ◽  
Chen Yang ◽  
Huanhuan Liu
Keyword(s):  
Time Delay ◽  
Market Price ◽  
Period Doubling ◽  
System Stability ◽  
Delayed Feedback Control ◽  
System Control ◽  
Heterogeneous Players ◽  
Cournot Game ◽  
The Stability ◽  
Time Delayed Feedback

Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price. The dynamics of both players output adjustments are analyzed and simulated. The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability. It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.

CONTROLLING BIFURCATION AND CHAOS IN INTERNET CONGESTION CONTROL MODEL

2004 ◽  
Vol 14 (05) ◽  
pp. 1863-1876 ◽  
Author(s):  
LIANG CHEN ◽  
XIAO FAN WANG ◽  
ZHENG ZHI HAN
Keyword(s):  
Congestion Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Parameter Tuning ◽  
Delayed Feedback Control ◽  
Bifurcation And Chaos ◽  
Adaptive Parameter ◽  
Discrete Time Dynamical System ◽  
Basic Features ◽  
Time Delayed Feedback

The TCP end-to-end congestion control plus RED router queue management can be modeled as a discrete-time dynamical system, which can create complex bifurcating and chaotic behavior. Based on the basic features of the TCP-RED model, we investigate the possibility of controlling bifurcation and chaos in the system via several time-delayed feedback control strategies. Two adaptive parameter-tuning algorithms are proposed and evaluated.

BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP

2013 ◽  
Vol 23 (08) ◽  
pp. 1330029 ◽  
Author(s):  
TANMOY BANERJEE ◽  
BISHWAJIT PAUL ◽  
B. C. SARKAR
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Parameter Space ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Convergence Time ◽  
Stable Phase ◽  
Bifurcation And Chaos ◽  
Global Parameter ◽  
Time Delayed Feedback

This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to find out the stable phase-locked zone of the system for both the controlled cases. We employ two-parameter bifurcation diagrams and the Lyapunov exponent spectrum to explore the dynamics of the system in the global parameter space. We establish that the control techniques can extend the stable phase-locked region of operation by controlling the occurrence of bifurcation and chaos. We also derive an estimate of the optimum parameter values for which the controlled system has the fastest convergence time even for a larger acquisition range. The present study provides a necessary detailed parameter space study that will enable one to design an improved TDTL system.

Stability and Bifurcation Analysis in a Maglev System with Multiple Delays

2015 ◽  
Vol 25 (05) ◽  
pp. 1550074 ◽  
Author(s):  
Lingling Zhang ◽  
Jianhua Huang ◽  
Lihong Huang ◽  
Zhizhou Zhang
Keyword(s):  
Time Delays ◽  
Dynamical Behavior ◽  
Delayed Feedback Control ◽  
Multiple Delays ◽  
Maglev System ◽  
Two Delays ◽  
Normal Form Method ◽  
The Stability ◽  
Manifold Theory ◽  
Time Delayed Feedback

This paper considers the time-delayed feedback control for Maglev system with two discrete time delays. We determine constraints on the feedback time delays which ensure the stability of the Maglev system. An algorithm is developed for drawing a two-parametric bifurcation diagram with respect to two delays τ1 and τ2. Direction and stability of periodic solutions are also determined using the normal form method and center manifold theory by Hassard. The complex dynamical behavior of the Maglev system near the domain of stability is confirmed by exhaustive numerical simulation.

Bifurcation to fronts due to delay

2010 ◽  
Vol 368 (1911) ◽  
pp. 483-493 ◽  
Author(s):  
T. Erneux ◽  
G. Kozyreff ◽  
M. Tlidi
Keyword(s):  
Global Bifurcation ◽  
Propagation Speed ◽  
Radial Symmetry ◽  
Delayed Feedback Control ◽  
The Past ◽  
The Difference ◽  
The Stability ◽  
System Variables ◽  
Time Delayed Feedback ◽  
Moving Front

The stability of a steady-state front (kink) subject to a time-delayed feedback control (TDFC) is examined in detail. TDFC is based on the use of the difference between system variables at the current moment of time and their values at some time in the past. We first show that there exists a bifurcation to a moving front. We then investigate the limit of large delays but weak feedback and obtain a global bifurcation diagram for the propagation speed. Finally, we examine the case of a two-dimensional front with radial symmetry and determine the critical radius above which propagation is possible.

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