scholarly journals Dynamic Effects Arise Due to Consumers’ Preferences Depending on Past Choices

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 173 ◽  
Author(s):  
Sameh S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Numerical Simulation ◽  
Fixed Points ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Dynamic Effects ◽  
One Dimensional ◽  
First Case ◽  
The Stability ◽  
Conditions Of Stability ◽  
Dynamic Duopoly

We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb–Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game’s map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game’s parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game’s map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case.

A Dynamic Duopoly Game with Content Providers’ Bounded Rationality

2020 ◽  
Vol 30 (07) ◽  
pp. 2050095 ◽  
Author(s):  
Hamid Garmani ◽  
Driss Ait Omar ◽  
Mohamed El Amrani ◽  
Mohamed Baslam ◽  
Mostafa Jourhmane
Keyword(s):  
Bounded Rationality ◽  
Chaotic Behavior ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Pricing Decisions ◽  
Dynamical Behaviors ◽  
Duopoly Model ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Dynamic Duopoly

This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs’ rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control.

Stability of synchronous regimes in unbalanced rotors on elastic base

2020 ◽  
pp. 095440622092032
Author(s):  
Arkadiy I Manevich
Keyword(s):  
Numerical Simulation ◽  
Parametric Instability ◽  
Elastic Base ◽  
First Approximation ◽  
Unbalanced Rotor ◽  
Synchronous Rotation ◽  
The Stability ◽  
Conditions Of Stability ◽  
Nonuniform Rotation ◽  
Driving Torque

The stationary dynamics of an unbalanced rotor (vibrator) on a movable base (linear oscillator) under excitation by a driving torque is studied with focusing on the stability of 1:1 stationary regimes of rotation and oscillation. This problem was well studied previously in the first approximation, dealing, in fact, with averaged regimes, mainly in the framework of asymptotic procedures. We use an efficient analytical procedure, proposed in our previous works for another problem, which sequentially separates the averaged regimes and deviations from them. Describing in the first approximation the known features of the synchronous stationary regimes under consideration, this approach in the second approximation results in the analytical solution for nonuniform rotation whose exactness is confirmed in the numerical simulation. The solution enables us to reveal possibility of parametric instability for oscillations of the rotor angular velocity and to describe two possible mechanisms of this instability. It is shown that the known condition of stability of stationary synchronous rotation-oscillation regimes is only necessary but not sufficient criterion, and two additional necessary conditions of stability are obtained and confirmed by the numerical simulation.

Shilnikov Chaos and Dynamics of a Self-Sustained Electromechanical Transducer

2000 ◽  
Vol 123 (2) ◽  
pp. 170-174 ◽  
Author(s):  
J. C. Chedjou ◽  
P. Woafo ◽  
S. Domngang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Critical Points ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
The Stability

The dynamics of a self-sustained electromechanical transducer is studied. The stability of the critical points is analyzed using the analytic Routh-Hurwitz criterion. Analytic oscillatory solutions are obtained in both the resonant and non-resonant cases. Chaotic behavior is observed using the Shilnikov theorem and from a direct numerical simulation of the equations of motion.

Global Dynamics and Synchronization in a Duopoly Game with Bounded Rationality and Consumer Surplus

2019 ◽  
Vol 29 (11) ◽  
pp. 1930031 ◽  
Author(s):  
Yinxia Cao ◽  
Wei Zhou ◽  
Tong Chu ◽  
Yingxiang Chang
Keyword(s):  
Bounded Rationality ◽  
Equilibrium Points ◽  
Logistic Map ◽  
Consumer Surplus ◽  
Global Dynamics ◽  
Bifurcation Diagrams ◽  
Fractal Structures ◽  
One Dimensional ◽  
Adjustment Speed ◽  
The Stability

Based on the oligopoly game theory, a dynamic duopoly Cournot model with bounded rationality and consumer surplus is established. On the one hand, the type and the stability of the boundary equilibrium points and the stability conditions of the Nash equilibrium point are discussed in detail. On the other hand, the potential complex dynamics of the system is demonstrated by a set of 2D bifurcation diagrams. It is found that the bifurcation diagrams have beautiful fractal structures when the adjustment speed of production is taken as the bifurcation parameter. And it is verified that the area with scattered points in the 2D bifurcation diagrams is caused by the coexistence of multiple attractors. It is also found that there may be two, three or four coexisting attractors. It is even found the coexistence of Milnor attractor and other attractors. Moreover, the topological structure of the attracting basin and global dynamics of the system are investigated by the noninvertible map theory, using the critical curve and the transverse Lyapunov exponent. It is concluded that two different types of global bifurcations may occur. Because of the symmetry of the system, it can be concluded that the diagonal of the system is an invariant one-dimensional submanifold. And it is controlled by a one-dimensional map which is equivalent to the classical Logistic map. The bifurcation curve of the system on the adjustment speed and the weight of the consumer surplus is obtained based on the properties of the Logistic map. And the synchronization phenomenon along the invariant diagonal is discussed at the end of the paper.

scholarly journals Dynamical properties of a novel one dimensional chaotic map

2022 ◽  
Vol 19 (3) ◽  
pp. 2489-2505
Author(s):  
Amit Kumar ◽  
◽  
Jehad Alzabut ◽  
Sudesh Kumari ◽  
Mamta Rani ◽  
...  
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Logistic Map ◽  
Maximal Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Dynamical Properties ◽  
Chaotic Logistic Map

<abstract><p>In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu &gt; 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.</p></abstract>

scholarly journals Van der Pol's oscillator under the parametric and forced excitations

2007 ◽  
Vol 29 (3) ◽  
pp. 207-219
Author(s):  
Nguyen Van Dao ◽  
Nguyen Van Dinh ◽  
Tran Kim Chi
Keyword(s):  
Small Parameter ◽  
Chaotic Behavior ◽  
Deterministic System ◽  
First Approximation ◽  
First Case ◽  
Oscillator Type ◽  
Resonance Curves ◽  
The Stability ◽  
The Given

Van der Pol's oscillator under parametric and forced excitations is studied. The case where the system contains a small parameter being quasilinear and the general case (without assumption on the smallness of nonlinear terms and perturbations) are studied. In the first case, equations of the first approximation are obtained by means of the Krylov-Bogoliubov-Mitropolskii technique, their averaging is performed, frequency amplitude and resonance curves are studied, on the stability of the given system is considered. In the second case, the possibility of chaotic behavior in a deterministic system of oscillator type is shown.

scholarly journals The Study of the Effect of Disease and Harvesting on Prey-Predator Interaction

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Nidhal Faisal Ali ◽  
Rami Raad Saadi
Keyword(s):  
Numerical Simulation ◽  
Fixed Points ◽  
Functional Response ◽  
Prey Species ◽  
Epidemiological Model ◽  
Global Dynamics ◽  
Predator Species ◽  
Unique Nature ◽  
External Sources ◽  
The Stability

This paper proposes and studies an eco-epidemiological model to describe the dynamic of the spread of a contagious illness of susceptible — infected — susceptible type. This model consists of prey-predator interaction, with the contagious illness in the predator species. It is supposed that, in addition to the existence of harvesting in the prey species and susceptible predator species, the contagious illness is spread only within the predator species through internal contact and external sources, and is not spread to the prey species. The functional response (Lotka-Volterra) is used to describe the Predator Capture. The existence of all fixed points are determined. The bounded and unique nature of the trajectory are proved. The stability (local and global) of all potential fixed points is studied. Finally, a more detailed investigation of the global dynamics of the proposed system is done with the help of numerical simulation.

scholarly journals ANALISIS KESTABILAN MODEL INTERAKSI PREDATOR-PREY DENGAN FUNGSI RESPON MONOD-HALDANE DAN PERILAKU ANTI PEMANGSA

2020 ◽  
Vol 8 (2) ◽  
pp. 51-59
Author(s):  
Muhammad Bachtiar Gaib ◽  
Wahdania At. Ja'a
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Predator Prey ◽  
First Case ◽  
Point Determination ◽  
Predator Model ◽  
The Stability ◽  
Predator Behavior

This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

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