scholarly journals Complex Dynamics in Nonlinear Triopoly Market with Different Expectations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Xiaosong Pu
Keyword(s):  
Local Stability ◽  
Demand Function ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Game Model ◽  
Bifurcation Diagrams ◽  
Nonlinear Difference Equations ◽  
Total Cost ◽  
Attractor Bifurcation ◽  
Total Cost Function

A dynamic triopoly game characterized by firms with different expectations is modeled by three-dimensional nonlinear difference equations, where the market has quadratic inverse demand function and the firm possesses cubic total cost function. The local stability of Nash equilibrium is studied. Numerical simulations are presented to show that the triopoly game model behaves chaotically with the variation of the parameters. We obtain the fractal dimension of the strange attractor, bifurcation diagrams, and Lyapunov exponents of the system.

COMPLEX DYNAMICS AND CHAOS CONTROL IN NONLINEAR FOUR-OLIGOPOLIST GAME WITH DIFFERENT EXPECTATIONS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350053 ◽  
Author(s):  
XIAOSONG PU ◽  
JUNHAI MA
Keyword(s):  
Local Stability ◽  
Chaos Control ◽  
Demand Function ◽  
Complex Dynamics ◽  
Parameter Variation ◽  
Variation Method ◽  
State Variables ◽  
Total Cost ◽  
Proposed Model ◽  
Total Cost Function

A dynamic four-oligopolist game characterized by firms with different expectations is modeled by four-dimensional nonlinear difference equations, where the market has a quadratic inverse demand function and the firm possesses a cubic total cost function. The Nash equilibrium of the local stability of the proposed model is studied. Then the bifurcation diagrams and Lyapunov exponents of the system are presented to show that four-oligopolist game model behaves chaotically with the variation of the parameters. Finally, the state variables' feedback and parameter variation method are effectively used to control the delay in the appearance of bifurcation.

scholarly journals Complex Dynamics of an Adnascent-Type Game Model

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Baogui Xin ◽  
Junhai Ma ◽  
Qin Gao
Keyword(s):  
Schwarzian Derivative ◽  
Complex Dynamics ◽  
Fractal Dimensions ◽  
Phase Portraits ◽  
Game Model ◽  
Bifurcation Diagrams ◽  
Bifurcation And Chaos ◽  
Normal Form Theory ◽  
Form Theory ◽  
Largest Lyapunov Exponents

The paper presents a nonlinear discrete game model for two oligopolistic firms whose products are adnascent. (In biology, the term adnascent has only one sense, “growing to or on something else,” e.g., “moss is an adnascent plant.” See Webster's Revised Unabridged Dictionary published in 1913 by C. & G. Merriam Co., edited by Noah Porter.) The bifurcation of its Nash equilibrium is analyzed with Schwarzian derivative and normal form theory. Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. At last, bifurcation and chaos anticontrol of this system are studied.

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 Analysis of Triopoly Game with Isoelastic Demand Function and Heterogeneous Players

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hong-Xing Yao ◽  
Lian Shi ◽  
Hao Xi
Keyword(s):  
Demand Function ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Game Model ◽  
Bifurcation Diagrams ◽  
Heterogeneous Players ◽  
Sensitive Dependence ◽  
Linear Demand ◽  
Isoelastic Demand Function ◽  
Asymptotic Stability Conditions

We analyze a triopoly game model with fully heterogeneous players when the demand function is isoelastic. The three players were considered to be bounded rational, adaptive, and naïve. Existing equilibrium points and their locally asymptotic stability conditions are studied. Complexity of the dynamical system is examined by means of numerical simulations, such as period cycles, bifurcation diagrams, strange attractors and sensitive, dependence on initial conditions. This paper extends the result of Tramontana (2010) who considered a heterogeneous duopoly with isoelastic demand function. Comparisons with respect to the heterogeneous triopoly model of Elabbasy et al. (2009) assuming linear demand function are performed.

scholarly journals Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 1 ◽  
Author(s):  
Han-Ping Hu ◽  
Jia-Kun Wang ◽  
Fei-Long Xie
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Hopfield Neural Network ◽  
Projective Synchronization ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Intermittent Chaos

In this paper, a new three-dimensional fractional-order Hopfield-type neural network with delay is proposed. The system has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable. Intermittent chaos is found in this system. The complex dynamics are analyzed both theoretically and numerically, including intermittent chaos, periodicity, and stability. Those phenomena are confirmed by phase portraits, bifurcation diagrams, and the Largest Lyapunov exponent. Furthermore, a synchronization method based on the state observer is proposed to synchronize a class of time-delayed fractional-order Hopfield-type neural networks.

Sustainable optimal ordering quantity for non-instantaneous deteriorating items under joint replenishment with substitution and carbon emission

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ranu Singh ◽  
Vinod Kumar Mishra
Keyword(s):  
Cost Function ◽  
Carbon Emission ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Joint Replenishment ◽  
Content Type ◽  
Total Cost ◽  
Optimal Ordering ◽  
Ordering Quantity ◽  
Total Cost Function

Purpose Carbon emission is a significant issue for the current business market and global warming. Nowadays, most countries have focused to reduce the environmental impact of business with durable financial benefits. The purpose of this study is to optimize the entire cost functions with carbon emission and to find the sustainable optimal ordering quantity for retailers. Design/methodology/approach This paper illustrates a sustainable inventory model having a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. In this model demand and deterioration rate are considered as deterministic, constant and triangular fuzzy numbers. The objective is to find the optimal ordering quantity for retailers and to minimize the total cost function per unit time with carbon emission. The model is then solved with the help of Maple software. Findings This paper presents a solution method and also develop an algorithm to determine the order quantities which optimize the total cost function. A numerical experiment illustrates the improvement in optimal total cost of the inventory model with substitution over without substitution. The graphical results show the convexity of the cost function. Finally, sensitivity analysis is given to get the impact of parameters and validity of the model. Originality/value This study considers a set of two non-instantaneous substitutable deteriorating items under joint replenishment with carbon emission. From the literature review, in the authors’ knowledge no researcher has undergone this kind of study.

scholarly journals Surface, size and topological effects for some nematic equilibria on rectangular domains

2020 ◽  
Vol 25 (5) ◽  
pp. 1101-1123 ◽  
Author(s):  
Lidong Fang ◽  
Apala Majumdar ◽  
Lei Zhang
Keyword(s):  
Aspect Ratio ◽  
Point Defects ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Variable Formula ◽  
Limiting Profile ◽  
Switching Dynamics ◽  
Line Defects ◽  
Carry Over

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, [Formula: see text], which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the [Formula: see text] 0 limit relevant for macroscopic domains and the [Formula: see text] limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the [Formula: see text] limit, whereas we observe fractional point defects in the [Formula: see text] 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of [Formula: see text] and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics.

scholarly journals Complex Dynamics of a Novel Chaotic System Based on an Active Memristor

Electronics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 410 ◽  
Author(s):  
Qinghai Song ◽  
Hui Chang ◽  
Yuxia Li
Keyword(s):  
Signal Processing ◽  
Complex Dynamics ◽  
Digital Signal ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
State Switching ◽  
Autonomous Differential Equations

On the basis of the bistable bi-local active memristor (BBAM), an active memristor (AM) and its emulator were designed, and the characteristic fingerprints of the memristor were found under the applied periodic voltage. A memristor-based chaotic circuit was constructed, whose corresponding dynamics system was described by the 4-D autonomous differential equations. Complex dynamics behaviors, including chaos, transient chaos, heterogeneous coexisting attractors, and state-switches of the system were analyzed and explored by using Lyapunov exponents, bifurcation diagrams, phase diagrams, and Poincaré mapping, among others. In particular, a novel exotic chaotic attractor of the system was observed, as well as the singular state-switching between point attractors and chaotic attractors. The results of the theoretical analysis were verified by both circuit experiments and digital signal processing (DSP) technology.

Three‐dimensional seismic exploration—A cost‐effective approach

Geophysics ◽  
1989 ◽  
Vol 54 (7) ◽  
pp. 815-823
Author(s):  
F. M. Peterson ◽  
W. C. Reynish
Keyword(s):  
Data Processing ◽  
Field Data ◽  
Three Dimensional ◽  
Cost Effective ◽  
Seismic Exploration ◽  
Effective Solution ◽  
Total Cost ◽  
Oil Companies ◽  
Cost Effective Approach ◽  
Data Field

Three‐dimensional (3-D) seismic prospecting is generally perceived as a very expensive tool that is not suitable for use by other than major oil companies or for the solution of conventional exploration geophysics problems. We illustrate how 3-D techniques were used to provide a very cost‐effective solution to a specific exploration project. A basic geologic and historical seismic outline establishes the economic and environmental framework for the survey. Drilling results and comparisons with conventional data illustrate the effectiveness of the 3-D approach. This survey was carried out during February of 1982 in the Black Creek basin of northwestern Alberta. Prolific and abundant Devonian Keg River pinnacle reefs with reserves in the 0.2 to 100 million barrel recoverable categories provide the exploration target. A prospective area of approximately [Formula: see text] was covered with a 165 ft subsurface grid of 1200 percent CDP data. Field data were acquired with a conventional 96-trace dynamite crew using a rolling, crossed‐array technique. Data processing was carried out with a flexible, conventional seismic processing package, including wavelet deconvolution, surface‐consistent statics, 3-D migration, and geologic slice displays. Total cost of the survey was $50,000 Canadian per sq mi. This paper demonstrates the interpretive power of 3-D surveys.

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