scholarly journals Critical bifurcation surfaces of 3D discrete dynamics

2000 ◽  
Vol 4 (4) ◽  
pp. 333-343 ◽  
Author(s):  
Michael Sonis
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Bifurcation Analysis ◽  
Analytical Representation ◽  
General Algorithm ◽  
Cournot Oligopoly ◽  
Adjustment Process ◽  
Discrete Dynamics ◽  
Oligopoly Model ◽  
Analytical Construction

This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of then-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction) of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.

scholarly journals Rational expectations and the Cournot-Theocharis problem

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Tönu Puu
Keyword(s):  
Fixed Point ◽  
Rational Expectations ◽  
Demand Function ◽  
Dynamic Models ◽  
The Other ◽  
Cournot Oligopoly ◽  
Trivial Case ◽  
Oligopoly Model ◽  
Marginal Costs ◽  
Linear Demand

In dynamic models in economics, often “rational expectations” are assumed. These are meant to show that the agents can correctly foresee the result of their own and the other agents' actions. In this paper, it is shown that this cannot happen in a simple oligopoly model with a linear demand function and constant marginal costs. “Naive expectations,” that is, where each agent assumes the other agents to retain their previous period action, are shown to result in a 2-period cycle. However, adapting to the observed periodicity always doubles the actual resulting periodicity. In general, it is impossible for the agents to learn any periodicity except the trivial case of a fixed point. This makes the whole idea of “rational expectations” untenable in Cournot oligopoly models.

scholarly journals Chaos Control and Anti-Control of the Heterogeneous Cournot Oligopoly Model

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1670
Author(s):  
Marek Lampart ◽  
Alžběta Lampartová
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Chaos Control ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Cournot Oligopoly ◽  
Maximal Lyapunov Exponent ◽  
Oligopoly Model ◽  
Chaos Suppression

The main aim of this paper focuses on chaos suppression (control) and stimulation (anti-control) of a heterogeneous Cournot oligopoly model. This goal is reached by applying the theory of dynamical systems, namely impulsive control. The main aim was to demonstrate, through massive numerical simulations and estimation of the maximal Lyapunov exponent, the 0-1test for chaos, and bifurcation analysis, that it is possible to control the dynamical behavior of the investigated model by finding injection values under which the desired phenomena are attained. Moreover, it was shown that there are injection values for which the injected system admits a self-excited cycle or chaotic trajectory.

scholarly journals Asymptotic Stability of Nonlinear Discrete Fractional Pantograph Equations with Non-Local Initial Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 473
Author(s):  
Jehad Alzabut ◽  
A. George Maria Selvam ◽  
Rami Ahmad El-Nabulsi ◽  
D. Vignesh ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Current Collector ◽  
Stability Of Solutions ◽  
Electric Bus ◽  
Pantograph Equation ◽  
Non Local

Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form Δ*β[k](t)=wt+β,k(t+β),k(λ(t+β)), with condition k(0)=p[k] for t∈N1−β, 0<β≤1, λ∈(0,1) and investigate the properties of asymptotic stability of solutions. We will prove the main results by the aid of Krasnoselskii’s and generalized Banach fixed point theorems. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

Customs Unions among Producing Countries with Different Costs

2009 ◽  
Vol 10 (1) ◽  
pp. 53-63
Author(s):  
Jose Mendez-Naya ◽  
Tomas Gomez-Arias
Keyword(s):  
Production Cost ◽  
Cournot Oligopoly ◽  
Customs Union ◽  
Customs Unions ◽  
Oligopoly Model ◽  
Consumer Country ◽  
Homogeneous Product ◽  
The One ◽  
Homogeneous Good

The effects of production cost asymmetries on the sustainability of customs unions among producing countries are investigated using a homogeneous-product Cournot oligopoly model, in which three producing countries subsidize exports of an homogeneous good to a consumer country that imposes a tariff on imports. It is found that the only sustainable customs union is the one formed by the three-member customs union. However, although the said customs union will be in equilibrium if utility transferences among member countries are allowed, it could not be in equilibrium if such transferences are not allowed.

scholarly journals An evolutionary Cournot oligopoly model with imitators and perfect foresight best responders

2019 ◽  
Vol 70 (3) ◽  
pp. 458-475 ◽  
Author(s):  
Lorenzo Cerboni Baiardi ◽  
Ahmad K. Naimzada
Keyword(s):  
Cournot Oligopoly ◽  
Perfect Foresight ◽  
Oligopoly Model

UNEMPLOYMENT IN AN EXTENDED COURNOT OLIGOPOLY MODEL

1989 ◽  
Vol 41 (1) ◽  
pp. 490-505 ◽  
Author(s):  
CLAUDE d'ASPREMONT ◽  
RODOLPHE DOS SANTOS FERREIRA ◽  
LOUIS-ANDRÉ GÉRARD-VARET
Keyword(s):  
Cournot Oligopoly ◽  
Oligopoly Model

GLOBAL BIFURCATIONS IN DUOPOLY WHEN THE COURNOT POINT IS DESTABILIZED VIA A SUBCRITICAL NEIMARK BIFURCATION

2006 ◽  
Vol 08 (01) ◽  
pp. 1-20 ◽  
Author(s):  
ANNA AGLIARI ◽  
LAURA GARDINI ◽  
TONU PUU
Keyword(s):  
Fixed Point ◽  
Equilibrium Point ◽  
Demand Function ◽  
Global Bifurcations ◽  
Cournot Equilibrium ◽  
Oligopoly Model ◽  
Marginal Costs

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive Cournot fixed point.

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