scholarly journals Research on a Dynamic Master-Slave Cournot Triopoly Game Model with Bounded Rational Rule and Its Control

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Hongliang Tu ◽  
Xinyu Wang
Keyword(s):  
Dynamical Systems ◽  
Phase Portrait ◽  
Bifurcation Theory ◽  
Initial Conditions ◽  
Stable Region ◽  
Game Model ◽  
Dynamical Behaviors ◽  
Sensitive Dependence ◽  
Adjustment Speed ◽  
Largest Lyapunov Exponents

The oligopoly market is modelled by a new dynamic master-slave Cournot triopoly game model with bounded rational rule. The local stabile conditions and the stable region are got by the dynamical systems bifurcation theory. The dynamics characteristics of the system with the changes of the adjustment speed parameters are analyzed by means of bifurcation diagram, largest Lyapunov exponents, phase portrait, and sensitive dependence on initial conditions. Furthermore, the parameters adjustment method is used to control the complex dynamical behaviors of the systems. The derived results have some important theoretical and practical meanings for the oligopoly market.

STUDY ON THE NONLINEAR VIBRATION OF SWCNTs WITH INITIAL AXIAL STRESS BASED ON THE BIFURCATION THEORY OF DYNAMICAL SYSTEMS

2010 ◽  
Vol 24 (18) ◽  
pp. 1979-1986
Author(s):  
YAN YAN ◽  
WENQUAN WANG ◽  
LIXIANG ZHANG
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Theory ◽  
Initial Conditions ◽  
Axial Stress ◽  
Sufficient Conditions ◽  
Homoclinic Orbits ◽  
Heteroclinic Orbits ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Families Of Periodic Orbits

The nonlinear dynamical behaviors of single-walled carbon nanotubes (SWCNTs) with the initial axial stress are investigated based on Donnell's cylindrical shell model. By using the bifurcation theory of dynamical systems on a vibration equation of SWCNTs, the existence of centers, saddles, families of periodic orbits, homoclinic orbits and/or heteroclinic orbits is shown. Under different initial conditions, various sufficient conditions to guarantee the existence of the above solutions are given and the dynamical behaviors of SWCNTs are well-known.

scholarly journals On some kinds of dense orbits in general nonautonomous dynamical systems

2020 ◽  
Vol 7 (1) ◽  
pp. 163-175
Author(s):  
Mehdi Pourbarat
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Point Of View ◽  
Topological Conjugacy ◽  
Topological Transitivity ◽  
Nonautonomous Systems ◽  
Nonautonomous Dynamical Systems ◽  
Sensitive Dependence ◽  
Dense Orbits

AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

scholarly journals Periodic Peakon and Smooth Periodic Solutions for KP-MEW(3,2) Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Junning Cai ◽  
Minzhi Wei ◽  
Liping He
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Dynamical Systems ◽  
Periodic Solutions ◽  
Phase Portrait ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Wave System ◽  
Integral Constant ◽  
Straight Line

In this paper, we consider the KP-MEW(3,2) equation by the bifurcation theory of dynamical systems when integral constant is considered. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. The phase portrait for c < 0 , 0 < c < 1 , and c > 1 is drawn. Exact parametric representations of periodic peakon solutions and smooth periodic solution are presented.

scholarly journals Dweiltime Analysis of Symmetry-Breaking Dynamical Systems

1995 ◽  
Vol 50 (12) ◽  
pp. 1117-1122 ◽  
Author(s):  
J. Vollmer ◽  
J. Peinke ◽  
A. Okniński
Keyword(s):  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Dwell Time ◽  
Initial Conditions ◽  
Dissipative Systems ◽  
Time Analysis ◽  
Chaotic Scattering ◽  
One Dimensional ◽  
Basin Boundary ◽  
Sensitive Dependence

Abstract Dweiltime analysis is known to characterize saddles giving rise to chaotic scattering. In the present paper it is used to characterize the dependence on initial conditions of the attractor approached by a trajectory in dissipative systems described by one-dimensional, noninvertible mappings which show symmetry breaking. There may be symmetry-related attractors in these systems, and which attractor is approached may depend sensitively on the initial conditions. Dwell-time analysis is useful in this context because it allows to visualize in another way the repellers on the basin boundary which cause this sensitive dependence.

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 A Study of Chaos in Dynamical Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
S. Effah-Poku ◽  
W. Obeng-Denteh ◽  
I. K. Dontwi
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Initial Conditions ◽  
Period Doubling ◽  
Dense Orbit ◽  
Routes To Chaos ◽  
Sensitive Dependence ◽  
Nonlinear Science

The behavior of systems such as periodicity, fixed points, and most importantly chaos has evolved as an integral part of mathematics, especially in dynamical system. This research presents a study on chaos as a property of nonlinear science. Systems with at least two of the following properties are considered to be chaotic in a certain sense: bifurcation and period doubling, period three, transitivity and dense orbit, sensitive dependence to initial conditions, and expansivity. These are termed as the routes to chaos.

scholarly journals Converging towards the optimal path to extinction

2011 ◽  
Vol 8 (65) ◽  
pp. 1699-1707 ◽  
Author(s):  
Ira B. Schwartz ◽  
Eric Forgoston ◽  
Simone Bianco ◽  
Leah B. Shaw
Keyword(s):  
Dynamical Systems ◽  
Random Process ◽  
Chemical Reactions ◽  
Stochastic Models ◽  
Population Biology ◽  
Initial Conditions ◽  
Optimal Path ◽  
Rare Event ◽  
Effective Force ◽  
Sensitive Dependence

Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite populations. Extinction occurs when fluctuations owing to random transitions act as an effective force that drives one or more components or species to vanish. Although there are many random paths to an extinct state, there is an optimal path that maximizes the probability to extinction. In this paper, we show that the optimal path is associated with the dynamical systems idea of having maximum sensitive dependence to initial conditions. Using the equivalence between the sensitive dependence and the path to extinction, we show that the dynamical systems picture of extinction evolves naturally towards the optimal path in several stochastic models of epidemics.

Sign in / Sign up

Export Citation Format

Share Document