scholarly journals Investigations of Nonlinear Triopoly Models with Different Mechanisms

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
S. S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Dynamical System ◽  
Global Analysis ◽  
Discrete Dynamical System ◽  
The Other ◽  
3 Dimensional ◽  
Heterogeneous Players ◽  
State Point ◽  
The Stability ◽  
The Impact ◽  
Nash Point

This paper studies the dynamic characteristics of triopoly models that are constructed based on a 3-dimensional Cobb–Douglas utility function. The paper presents two parts. The first part introduces a competition among three rational firms on which their prices are isoelastic functions. The competition is described by a 3-dimensional discrete dynamical system. We examine the impact of rationality on the system’s steady state point. Studying the stability/instability of this point, which is Nash equilibrium and is unique in those models, is illustrated. Numerically, we give some global analysis of Nash point and its stability. The second part deals with heterogeneous scenarios. It consists of two different models. In the first model, we assume that one competitor adopts the local monopolistic approximation mechanism (LMA) while the other opponents are rational. The second model assumes two heterogeneous players with LMA mechanism against one rational firm. Studies show that the stability of NE point of those models is not guaranteed. Furthermore, simulation shows that when firms behave rational with symmetric costs, the stability of NE point is achievable.

Three Conditions Lyapunov Exponents Should Satisfy

2003 ◽  
Author(s):  
Jingjun Lou ◽  
Shijian Zhu
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic Motion ◽  
The Other ◽  
Cubic Nonlinearity ◽  
3 Dimensional ◽  
Duffing System ◽  
Dissipative Dynamical System

In contrast to the unilateral claim in some papers that a positive Lyapunov exponent means chaos, it was claimed in this paper that this is just one of the three conditions that Lyapunov exponent should satisfy in a dissipative dynamical system when the chaotic motion appears. The other two conditions, any continuous dynamical system without a fixed point has at least one zero exponent, and any dissipative dynamical system has at least one negative exponent and the sum of all of the 1-dimensional Lyapunov exponents id negative, are also discussed. In order to verify the conclusion, a MATLAB scheme was developed for the computation of the 1-dimensional and 3-dimensional Lyapunov exponents of the Duffing system with square and cubic nonlinearity.

scholarly journals Intra-layer Synchronization in a Duplex Networks with Noise

2021 ◽  
Author(s):  
Jinsen Zhuang ◽  
Yan Zhou ◽  
Yonghui Xia
Keyword(s):  
Dynamical System ◽  
State Feedback ◽  
Feedback Controller ◽  
The Other ◽  
Time Varying ◽  
Stochastic Perturbations ◽  
State Feedback Controller ◽  
Control Schemes ◽  
Simulation Results ◽  
The Impact

This paper concerns the impact of stochastic perturbations on the intra-layer synchronization of the duplex networks. A duplex network contains two layers ([1,2]). Different from the previous works, environmental noise is introduced into the dynamical system of the duplex network. We incorporate both the inter-layer delay and the intra-layer delay into the dynamical system. Both of the delays are time-varying. However, the paper [1] only considered the intra-layer delays and they are assumed as the constants. While the paper [2] did not consider the inter-layer delay or intra-layer delay. When the system does not achieve automatic intra-layer synchronization, we introduce two controllers: one is the state-feedback controller, the other is the adaptive state-feedback controller. Interestingly, we find that the intra-layer synchronization will achieve automatically if the inter-layer coupling strength $c_1$ is large enough when the time-varying inter-layer delays are absent. Finally, some interesting simulation results are obtained for the Chua-Chua chaotic system with application of our theoretic results, which show the feasibility effectiveness of our control schemes.

THE INSTABILITY OF OPEN PARETO EFFICIENT ECONOMIES

2020 ◽  
pp. 1-36
Author(s):  
Antoine Le Riche
Keyword(s):  
Free Trade ◽  
The Other ◽  
Investment Good ◽  
Consumption Good ◽  
Elasticity Of Intertemporal Substitution ◽  
Equilibrium Indeterminacy ◽  
The Stability ◽  
The One ◽  
The Impact ◽  
Capital Intensive

This paper analyzes the impact of trade on the stability properties of trading countries and on stationary welfare. We consider a two-country two-good two-factor overlapping generations model where countries differ in terms of their technology. In the autarky equilibrium and the free-trade equilibrium, indeterminacy relies, under dynamic efficiency, on a capital intensive consumption good and intermediate values of the elasticity of intertemporal substitution in consumption. Opening the borders to trade can be a source of a global destabilizing effect. Indeed, considering a free-trade equilibrium in which one country is an exporter of the consumption good and the other country is an exporter of the investment good, indeterminacy can occur with trade even though the two countries are determinate in autarky. Finally, opening to trade increases the stationary welfare of the country that exports the investment good and deteriorates the one of the other country.

scholarly journals Global asymptotic stability of inhomogeneous iterates

2002 ◽  
Vol 29 (3) ◽  
pp. 133-142 ◽  
Author(s):  
Yong-Zhuo Chen
Keyword(s):  
Dynamical System ◽  
Asymptotic Stability ◽  
Metric Space ◽  
Complete Metric Space ◽  
Discrete Dynamical System ◽  
Closed Convex Cone ◽  
Nonlinear Difference Equations ◽  
Finite Dimensional ◽  
Uniformly Convergent ◽  
The Stability

Let(M,d)be a finite-dimensional complete metric space, and{Tn}a sequence of uniformly convergent operators onM. We study the non-autonomous discrete dynamical systemxn+1=Tnxnand the globally asymptotic stability of the inhomogeneous iterates of{Tn}. Then we apply the results to investigate the stability of equilibrium ofTwhen it satisfies certain type of sublinear conditions with respect to the partial order defined by a closed convex cone. The examples of application to nonlinear difference equations are also given.

The impact of flexibility of polyimides backbones on the stability of liquid crystal vertical alignment

RSC Advances ◽  
2016 ◽  
Vol 6 (60) ◽  
pp. 55479-55489 ◽  
Author(s):  
Xinyuan Che ◽  
Shiming Gong ◽  
Leishan Shao ◽  
Tian Lan ◽  
Fei Wang ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
The Other ◽  
Side Chain ◽  
Vertical Alignment ◽  
The Stability ◽  
The Impact ◽  
Chain Type

Two side-chain-type polyimides (RPI and SPI) containing different backbones induced vertical alignments of liquid crystals, after rubbing, one maintained stable vertical, while the other transformed from vertical into parallel.

STABILITY ANALYSIS OF A DISCRETE NONLINEAR DELAY SURVIVAL RED BLOOD CELLS MODEL

2012 ◽  
Vol 05 (04) ◽  
pp. 1250030
Author(s):  
SHUFANG MA ◽  
YUANGANG ZU
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Discrete Dynamical System ◽  
Original System ◽  
Discrete Delay ◽  
The Stability ◽  
Stability Results ◽  
Nonlinear Delay

In this article we consider the kth-order discrete delay survival red blood cells model. The general form of the discrete dynamical system is rewritten as xn+1 = f(Pn, δn, xn, …, xn+1) where Pn, δn converge to the parametric values P and δ. We show that when the parameters are replaced by sequences, the stability results of the original system still hold.

scholarly journals On Dynamic Investigations of Cournot Duopoly Game: When Firms Want to Maximize Their Relative Profits

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2235
Author(s):  
Sameh Askar
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Utility Function ◽  
Global Analysis ◽  
Asymmetric Structure ◽  
Two Dimensional ◽  
Cournot Duopoly ◽  
The Stability ◽  
Nash Point ◽  
Discrete Map

This paper studies a Cournot duopoly game in which firms produce homogeneous goods and adopt a bounded rationality rule for updating productions. The firms are characterized by an isoelastic demand that is derived from a simple quadratic utility function with linear total costs. The two competing firms in this game seek the optimal quantities of their production by maximizing their relative profits. The model describing the game’s evolution is a two-dimensional nonlinear discrete map and has only one equilibrium point, which is a Nash point. The stability of this point is discussed and it is found that it loses its stability by two different ways, through flip and Neimark–Sacker bifurcations. Because of the asymmetric structure of the map due to different parameters, we show by means of global analysis and numerical simulation that the nonlinear, noninvertible map describing the game’s evolution can give rise to many important coexisting stable attractors (multistability). Analytically, some investigations are performed and prove the existence of areas known in literature with lobes.

scholarly journals Mutation and Chaos in Nonlinear Models of Heredity

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nasir Ganikhodjaev ◽  
Mansoor Saburov ◽  
Ashraf Mohamed Nawi
Keyword(s):  
Dynamical System ◽  
Nonlinear Models ◽  
Single Gene ◽  
Discrete Dynamical System ◽  
Mendelian Inheritance ◽  
The Other ◽  
New Generation

We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models.

Enduring Burmese Realities

2017 ◽  
Author(s):  
Renaud Egreteau
Keyword(s):  
National Economy ◽  
The Other ◽  
Moving Target ◽  
Realistic Assessment ◽  
The Stability ◽  
The Military ◽  
The Impact ◽  
National Reconciliation ◽  
India And China

This chapter seeks to provide a realistic assessment of the other long-term challenges that continue to plague Myanmar. While many are not necessarily hindering democratization, all pose considerable threats to the stability of the country and the long-term process of national reconciliation. Prominent among them is the multifaceted political and social clientelisms that are entrenched in Burmese society. Such is the case for the oligarchical structuration and weaknesses of the national economy, as well as Myanmar’s peculiar geography. This chapter looks at why the country cannot avoid considering the impact that its geopolitical situation has long imposed on its domestic developments. Myanmar’s position at the crossroads of India and China, where politics remains volatile and democratic consolidation is an endlessly moving target, may provide the military with incentives to remain involved in politics.

scholarly journals Effects of the Layer Height and Exposure Energy on the Lateral Resolution of Zirconia Parts Printed by Lithography-Based Additive Manufacturing

Materials ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1317 ◽  
Author(s):  
Laura Conti ◽  
Daniel Bienenstein ◽  
Mario Borlaf ◽  
Thomas Graule
Keyword(s):  
Additive Manufacturing ◽  
Layer Thickness ◽  
Layer By Layer ◽  
Layer Height ◽  
3 Dimensional ◽  
Stable Part ◽  
The Stability ◽  
Exposure Energy ◽  
The Impact ◽  
Am Processes

Lithography-based ceramics manufacturing (LCM) processes enable the sophisticated 3 dimensional (3D) shaping of ceramics by additive manufacturing (AM). The build-up occurs, like many other AM processes, layer by layer, and is initiated by light. The built-in digital mirror device (DMD) enables the specific exposure of desired pixels for every layer, giving as a consequence a first estimation of the printing resolution in the x and y axes. In this work, a commercial zirconia slurry and the CeraFab 7500, both from Lithoz GmbH (Vienna, Austria), were used to investigate the potential of reaching this resolution. The results showed that the precision of a part is strongly dependent on the applied exposure energy. Higher exposure energies resulted in oversized dimensions of a part, whereas too low energy was not able to guarantee the formation of a stable part. Furthermore, the investigation of the layer thickness showed that the applied exposure energy (mJ/cm2) was acting in a volume, and the impact is visible in x, y, and z dimensions. The lowest applied exposure energy was 83 mJ/cm2 and showed the most accurate results for a layer thickness of 25 μm. With this energy, holes and gaps smaller than 500 μm could be printed; however, the measurements differed significantly from the dimensions defined in the design. Holes and gaps larger than 500 μm showed deviations smaller than 50 μm from the design and could be printed reliably. The thinnest printable gaps were between 100 and 200 μm. Concerning the wall thickness, the experiments were conducted to a height of 1 cm. Taking into account the stability and deformation of the walls as well, the best results after sintering were achieved with thicknesses of 200–300 μm.

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