scholarly journals Global and Local Analysis for a Cournot Duopoly Game with Two Different Objective Functions

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3119
Author(s):  
Sameh Askar ◽  
Abdulaziz Foul ◽  
Tarek Mahrous ◽  
Saleh Djemele ◽  
Emad Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Logistic Map ◽  
Analytical Form ◽  
Local Analysis ◽  
Flip Bifurcation ◽  
Objective Functions ◽  
Critical Curves ◽  
Cournot Game ◽  
Bifurcation Phenomena ◽  
Global And Local

In this paper, a Cournot game with two competing firms is studied. The two competing firms seek the optimality of their quantities by maximizing two different objective functions. The first firm wants to maximize an average of social welfare and profit, while the second firm wants to maximize their relative profit only. We assume that both firms are rational, adopting a bounded rationality mechanism for updating their production outputs. A two-dimensional discrete time map is introduced to analyze the evolution of the game. The map has four equilibrium points and their stability conditions are investigated. We prove the Nash equilibrium point can be destabilized through flip bifurcation only. The obtained results show that the manifold of the game’s map can be analyzed through a one-dimensional map whose analytical form is similar to the well-known logistic map. The critical curves investigations show that the phase plane of game’s map is divided into three zones and, therefore, the map is not invertible. Finally, the contact bifurcation phenomena are discussed using simulation.

Dynamic Evolution, Synchronization and Multistability in an Advertising Game Model with Homogeneous Products and Spillover Effect

2020 ◽  
Vol 30 (10) ◽  
pp. 2050144 ◽  
Author(s):  
Wenrui Wang ◽  
Wei Zhou ◽  
Libin Xia
Keyword(s):  
Invariant Manifolds ◽  
Equilibrium Points ◽  
Logistic Map ◽  
Spillover Effect ◽  
Spillover Effects ◽  
Corporate Advertising ◽  
Dynamical Behaviors ◽  
Cournot Game ◽  
Advertising Effort ◽  
The Impact

Advertising competition among firms may give rise to very complex dynamical behaviors. In this article, under the assumption of spillover effects, a two-stage dynamical Cournot game of advertising competition between two firms, which produce homogeneous products, is developed. Then, the local stability of the equilibrium points is discussed, and stability conditions of the equilibrium points are obtained. In order to reveal the complex dynamical behaviors of the model, both analytical and numerical methods are employed. The research results show that the two coordinate axes and the diagonal of the system are invariant manifolds, and one can obtain the dynamical behaviors on the invariant manifolds by analyzing the Logistic map. In addition, it is found that the advertising efforts of these two firms may be synchronized, even if the system is in a chaotic state. Multistability is another topic of focus. It is found that not only two attractors but also three attractors can coexist in the phase space, and contact bifurcation can also occur during the evolution of the attracting basins. Finally, the impact of corporate advertising efforts on corporate profits is analyzed. It is found that too much advertising effort is harmful to the firms, and a firm with low adjustment speed can even earn more when the system is chaotic.

Adaptive Query Refinement Based on Global and Local Analysis

2005 ◽  
pp. 584-593 ◽  
Author(s):  
Chaoyuan Cui ◽  
Hanxiong Chen ◽  
Kazutaka Furuse ◽  
Nobuo Ohbo
Keyword(s):  
Local Analysis ◽  
Query Refinement ◽  
Global And Local

scholarly journals Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1458 ◽  
Author(s):  
Sameh S Askar ◽  
Abdulrahman Al-Khedhairi
Keyword(s):  
Complex Dynamics ◽  
Market Competition ◽  
Equilibrium Points ◽  
Profit Maximization ◽  
Stable Complex ◽  
Global Dynamics ◽  
Limited Information ◽  
Critical Curves ◽  
Local And Global Dynamics ◽  
Realistic Situation

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.

scholarly journals Energy Landscape of the SARS-CoV-2 Reveals Extensive Conformational Heterogeneity

2021 ◽  
Author(s):  
Ghoncheh Mashayekhi ◽  
John Vant ◽  
Abhishek Singharoy ◽  
Abbas Ourmazd
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Binding Pocket ◽  
Minimum Free Energy ◽  
Spike Protein ◽  
Local Analysis ◽  
Interaction Sites ◽  
Density Maps ◽  
The Stability ◽  
Global And Local

Cryo-electron microscopy (cryo-EM) has produced a number of structural models of the SARS-CoV-2 spike, already prompting biomedical outcomes. However, these reported models and their associated electrostatic potential maps represent an unknown admixture of conformations stemming from the underlying energy landscape of the spike protein. As for any protein, some of the spike's conformational motions are expected to be biophysically relevant, but cannot be interpreted only by static models. Using experimental cryo-EM images, we present the energy landscape of the spike protein conformations, and identify molecular rearrangements along the most-likely conformational path in the vicinity of the open (so called 1RBD-up) state. The resulting global and local atomic refinements reveal larger movements than those expected by comparing the reported 1RBD-up and 1RBD-down cryo-EM models. Here we report greater degrees of "openness" in global conformations of the 1RBD-up state, not revealed in the single-model interpretations of the density maps, together with conformations that overlap with the reported models. We discover how the glycan shield contributes to the stability of these conformations along the minimum free-energy pathway. A local analysis of seven key binding pockets reveals that six out them, including those for engaging ACE2, therapeutic mini-proteins, linoleic acid, two different kinds of antibodies, and protein-glycan interaction sites, switch conformations between their known apo- and holo-conformations, even when the global spike conformation is 1RBD-up. This is reminiscent of a conformational pre-equilibrium. We found only one binding pocket, namely antibody AB-C135 to remain closed along the entire minimum free energy path, suggesting an induced fit mechanism for this enzyme.

scholarly journals Local and global analysis of macromolecular atomic displacement parameters

2020 ◽  
Vol 76 (10) ◽  
pp. 926-937
Author(s):  
Rafiga C. Masmaliyeva ◽  
Kave H. Babai ◽  
Garib N. Murshudov
Keyword(s):  
Global Analysis ◽  
Expectation Maximization Algorithm ◽  
Atomic Displacement ◽  
Local Analysis ◽  
X Ray Crystallography ◽  
Inverse Gamma ◽  
Metal Atoms ◽  
Atomic Displacement Parameters ◽  
Global And Local ◽  
Validation Tool

This paper describes the global and local analysis of atomic displacement parameters (ADPs) of macromolecules in X-ray crystallography. The distribution of ADPs is shown to follow the shifted inverse-gamma distribution or a mixture of these distributions. The mixture parameters are estimated using the expectation–maximization algorithm. In addition, a method for the resolution- and individual ADP-dependent local analysis of neighbouring atoms has been designed. This method facilitates the detection of mismodelled atoms, heavy-metal atoms and disordered and/or incorrectly modelled ligands. Both global and local analyses can be used to detect errors in atomic models, thus helping in the (re)building, refinement and validation of macromolecular structures. This method can also serve as an additional validation tool during PDB deposition.

scholarly journals AN ALGORITHM FOR OBTAINING THE OPTIMAL GUARANTEED RESULT FOR OBJECTS WITH EXTREME CONDITIONS

2020 ◽  
Vol 72 (4) ◽  
pp. 34-40
Author(s):  
А.Е. Ismayilov ◽  
◽  
Zh. Kozhamkulova ◽  
M. Serikuly ◽  
◽  
...  
Keyword(s):  
Information Technology ◽  
Objective Function ◽  
Control Strategy ◽  
Rational Solution ◽  
Optimal Solution ◽  
Analytical Form ◽  
Extreme Conditions ◽  
Objective Functions ◽  
Existence Of A Solution ◽  
Multicriteria Problem

In this paper, an algorithm for obtaining the optimal guaranteed result for objects with extreme states is developed, based on the establishment of the function and functionals of an analytical form. The methodology for choosing a control strategy for an object with the best guaranteed result is described. The essence of the technique is to find an optimal solution to a multicriteria problem that maximizes the values of all functions. At the same time, the existence of a solution that literally maximizes all objective functions is a rare exception. The problem of obtaining a guaranteed result and the study of the possibility of its improvement, as well as the problem of choosing a rational solution were considered. It has been established that a strategy that has an efficiency estimate in a given operation equal to the best (largest) guaranteed result is the optimal guaranteeing strategy. The objective function has been determined, and an optimally guaranteed strategy has been undertaken for the management of biotechnological industries using information technology.

scholarly journals Determining Asymptotic Stability and Robustness of Networked Systems

Systems ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 39
Author(s):  
Elias August
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium Points ◽  
Rational Functions ◽  
Computational Method ◽  
Multiple Equilibrium ◽  
Local Analysis ◽  
Stable Equilibrium Point ◽  
Continuous Stirred Tank Reactor ◽  
Novel Approach ◽  
Individual System

This paper is motivated by the notion that coupling systems allows for mitigating the failure of individual ones. We present a novel approach to determining asymptotic stability and robustness of a network consisting of coupled dynamical systems, where individual system dynamics are represented through polynomial or rational functions. The analysis relies on a local analysis; thus, making it computationally implementable. We present an efficient computational method that relies on semidefinite programming. Importantly, for cases where multiple equilibrium points exist, we show how to determine regions around an asymptotically stable equilibrium point that bounds solutions. These regions increase when systems are coupled as we observe when applying the presented analysis framework to a mathematical model of a continuous stirred tank reactor. Importantly, the presented work has implications to other fields as well.

A Computerised Method For The Rapid Global and Local Analysis of Ship Structures

1998 ◽  
Author(s):  
K F Stone ◽  
◽  
R Kumar ◽  
N Pegg ◽  
D Heath ◽  
...  
Keyword(s):  
Local Analysis ◽  
Ship Structures ◽  
Global And Local

CHUA’S EQUATION WITH CUBIC NONLINEARITY

1996 ◽  
Vol 06 (12a) ◽  
pp. 2175-2222 ◽  
Author(s):  
ANSHAN HUANG ◽  
LADISLAV PIVKA ◽  
CHAI WAH WU ◽  
MARTIN FRANZ
Keyword(s):  
Computer Program ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Tabular Form ◽  
Cubic Nonlinearity ◽  
Bifurcation Phenomena ◽  
Hands On ◽  
Autonomous Differential Equations ◽  
Parameter Values

In this tutorial paper we present one of the simplest autonomous differential equations capable of generating chaotic behavior. Some of the fundamental routes to chaos and bifurcation phenomena are demonstrated with examples. A brief discussion of equilibrium points and their stability is given. For the convenience of the reader, a short computer program written in QuickBASIC is included to give the reader a possibility of quick hands-on experience with the generation of chaotic phenomena without using sophisticated numerical simulators. All the necessary parameter values and initial conditions are provided in a tabular form. Eigenvalue diagrams showing regions with particular eigenvalue patterns are given.

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