scholarly journals A Dynamic Duopoly Cournot Model with R&D Efforts and Its Dynamic Behavior Analysis

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Wei Zhou ◽  
Jie Zhou ◽  
Tong Chu ◽  
Hui Li
Keyword(s):  
Dynamic Behavior ◽  
Equilibrium Points ◽  
Flip Bifurcation ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Coexistence Of Attractors ◽  
Route To Chaos ◽  
The Stability ◽  
The Given ◽  
Jury Criterion

In this paper, a dynamic two-stage Cournot duopoly game with R&D efforts is built. Then, the local stability of the equilibrium points are discussed, and the stability condition of the Nash equilibrium point is also deduced through Jury criterion. The complex dynamical behaviors of the built model are investigated by numerical simulations. We found that the unique route to chaos is flip bifurcation, and the increase of adjusting speed will cause the system to lose stability and produce more complex dynamic behavior. In addition, we also found the phenomenon of multistability in the given model. Several kinds of coexistence of attractors are shown. In particular, we found that boundary attractors can coexist with internal attractors, which also aggravates the complexity of the system. At last, the chaotic state in the built system has been successfully controlled.

scholarly journals Autonomous Jerk Oscillator with Cosine Hyperbolic Nonlinearity: Analysis, FPGA Implementation, and Synchronization

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Sifeu Takougang Kingni ◽  
Gaetan Fautso Kuiate ◽  
Victor Kamdoum Tamba ◽  
Viet-Thanh Pham
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Phase Portraits ◽  
Adaptive Sliding Mode Control ◽  
Coexistence Of Attractors ◽  
Route To Chaos ◽  
Two Parameters

A two-parameter autonomous jerk oscillator with a cosine hyperbolic nonlinearity is proposed in this paper. Firstly, the stability of equilibrium points of proposed autonomous jerk oscillator is investigated by analyzing the characteristic equation and the existence of Hopf bifurcation is verified using one of the two parameters as a bifurcation parameter. By tuning its two parameters, various dynamical behaviors are found in the proposed autonomous jerk oscillator including periodic attractor, one-scroll chaotic attractor, and coexistence between chaotic and periodic attractors. The proposed autonomous jerk oscillator has period-doubling route to chaos with the variation of one of its parameters and reverse period-doubling route to chaos with the variation of its other parameter. The proposed autonomous jerk oscillator is modelled on Field Programmable Gate Array (FPGA) and the FPGA chip statistics and phase portraits are derived. The chaotic and coexistence of attractors generated in the proposed autonomous jerk oscillator are confirmed by FPGA implementation of the proposed autonomous jerk oscillator. A good qualitative agreement is illustrated between the numerical and FPGA results. Finally synchronization of unidirectional coupled identical proposed autonomous jerk oscillators is achieved using adaptive sliding mode control method.

Mathematical Modeling and Stability Analysis of Japanese Encephalitis

2020 ◽  
Vol 12 (1) ◽  
pp. 120-127
Author(s):  
Vinod Baniya ◽  
Ram Keval
Keyword(s):  
Mathematical Modeling ◽  
Japanese Encephalitis ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Numerical Verification ◽  
Transmission Potential ◽  
Dynamical Behaviors ◽  
Proposed Model ◽  
The Stability ◽  
Stability Issues

Mathematical modeling of Japanese encephalitis (JE) disease in human population with pig and mosquito has been presented in this paper. The proposed model, which involves three compartments of human (Susceptible, Vaccinated, Infected), two compartments of mosquito (Susceptible, Infected) and three compartments of the pig (Susceptible, Vaccinated, Infected). In this work, it is assumed that JE spreads between susceptible class and infected mosquitoes only. Basic results like boundedness of the model, the existence of equilibrium and local stability issues are investigated. Here, to measure the disease transmission potential in the population the basic reproduction number (R0) from the system has been analyzed w.r.t. control parameters both numerically and theoretically. The dynamical behaviors of the system have been analyzed by using the stability theory of differential equations and numerical simulations at equilibrium points. A numerical verification of results is carried out of the model under consideration.

scholarly journals Dynamic Cournot Duopoly Game with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Local Stability ◽  
Stability Region ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Delayed System

The delay Cournot duopoly game is studied. Dynamical behaviors of the game are studied. Equilibrium points and their stability are studied. The results show that the delayed system has the same Nash equilibrium point and the delay can increase the local stability region.

Dynamical analysis of fractional-order differentiated Cournot triopoly game

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1367-1380
Author(s):  
Abdulrahman Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Periodic Forcing ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Theoretical Results

The objective of the article is to study the dynamics of the proposed fractional-order Cournot triopoly game. Sufficient conditions for the existence and uniqueness of the triopoly game solution are obtained. Stability analysis of equilibrium points of the fractional-order game is also discussed. The conditions for the presence of Nash equilibrium point along with its global stability analysis are studied. The interesting dynamical behaviors of the arbitrary-order Cournot triopoly game are discussed. Moreover, the effects of seasonal periodic forcing on the game’s behaviors are examined. The 0–1 test is used to distinguish between regular and irregular dynamics of system behaviors. Numerical analysis is used to verify the theoretical results that are obtained, and revealed that the nonautonomous fractional-order model induces more complicated dynamics in the Cournot triopoly game behavior and the seasonally forced game exhibits more complex dynamics than the unforced one.

scholarly journals Dynamical Analysis of SIR Epidemic Models with Distributed Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Wencai Zhao ◽  
Tongqian Zhang ◽  
Zhengbo Chang ◽  
Xinzhu Meng ◽  
Yulin Liu
Keyword(s):  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Epidemic Models ◽  
Dynamical Analysis ◽  
Sir Epidemic ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Sir Epidemic Models

SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction numberRis got. In order to study the important role of vaccination to prevent diseases, the model with distributed delay under impulsive vaccination is formulated. And the sufficient conditions of globally asymptotic stability of “infection-free” periodic solution and the permanence of the model are obtained by using Floquet’s theorem, small-amplitude perturbation skills, and comparison theorem. Lastly, numerical simulation is presented to illustrate our main conclusions that vaccination has significant effects on the dynamical behaviors of the model. The results can provide effective tactic basis for the practical infectious disease prevention.

The effect of price discrimination on dynamic duopoly games with bounded rationality

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Qi-Qing Song ◽  
Wei-li Zhang ◽  
Yi-Rong Jiang ◽  
Juan Geng
Keyword(s):  
Bounded Rationality ◽  
Price Discrimination ◽  
Equilibrium Points ◽  
Dynamic Game ◽  
Stationary Points ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Demand Elasticities ◽  
The Stability ◽  
Dynamic Duopoly

AbstractIn a homogenous product market, customers’ different demand elasticities may lead to different prices. This study examined price discrimination’s effect on equilibrium points in Cournot duopoly games by assuming that each firm charges K prices and adjusts its strategies based on bounded rationality. In consideration of price discrimination, two discrete dynamic game systems with 2K variables were introduced for players with homogenous or heterogenous expectations. The stability of the Nash equilibrium point was found to be independent of price discrimination. Given price discrimination, the stability of boundary stationary points for the system with homogenous players is different from that for the system with heterogenous players. Numerical simulations verified the critical point for the system with homogenous players from being stable to its bifurcation.

scholarly journals Symbolic Methods for Analysing Bifurcations and Chaos of Two Five-Parameter Families of Planar Quadratic Maps

2020 ◽  
Vol 8 (2) ◽  
pp. 72-79
Author(s):  
Sarbast H. Mikaeel ◽  
Bewar H. Othman
Keyword(s):  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Algorithmic Approach ◽  
Quadratic Maps ◽  
Dynamical Behaviors ◽  
Planar Maps ◽  
Symbolic Methods ◽  
The Stability

In this work, we analyze the dynamical behaviors of two five-parameter families of planar quadratic maps by utilizing strategies of symbolic computation. We are going to use computer algebra methods to clarify how to detect the stability of equilibrium points to analyze chaos and also the bifurcation of planar maps. Based on strategies for solving the systems in types of semi-algebraic and by utilizing an algorithmic approach, we obtain respectively for the two maps, sufficient conditions on the parameters to have a prescribed number of (stable) equilibrium points; necessary conditions on the parameters to undergo a certain type of bifurcation or to have chaotic behavior induced by snapback repeller.

scholarly journals Complexity Analysis of a 3-Player Game with Bounded Rationality Participating in Nitrogen Emission Reduction

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Jixiang Zhang ◽  
Xuan Xi
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Bounded Rationality ◽  
Control Method ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Stable Region ◽  
Nitrogen Emissions ◽  
Nash Equilibrium Point ◽  
The Stability

In this paper, a decision-making competition game model concerning governments, agricultural enterprises, and the public, all of which participate in the reduction of nitrogen emissions in the watersheds, is established based on bounded rationality. First, the stability conditions of the equilibrium points in the system are discussed, and the stable region of the Nash equilibrium is determined. Then, the bifurcation diagram, maximal Lyapunov exponent, strange attractor, and sensitive dependence on the initial conditions are shown through numerical simulations. The research shows that the adjustment speed of three players’ decisions may alter the stability of the Nash equilibrium point and lead to chaos in the system. Among these decisions, a government’s decision has the largest effect on the system. In addition, we find that some parameters will affect the stability of the system; when the parameters become beneficial for enterprises to reduce nitrogen emissions, the increase in the parameters can help control the chaotic market. Finally, the delay feedback control method is used to successfully control the chaos in the system and stabilize it at the Nash equilibrium point. The research of this paper is of great significance to the environmental governance decisions and nitrogen reduction management.

COMPLEX DYNAMICAL ANALYSIS OF A COUPLED NETWORK FROM INNATE IMMUNE RESPONSES

2013 ◽  
Vol 23 (11) ◽  
pp. 1350180 ◽  
Author(s):  
JINYING TAN ◽  
XIUFEN ZOU
Keyword(s):  
Immune Responses ◽  
Negative Feedback ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Innate Immune ◽  
Dynamical Analysis ◽  
Innate Immune Responses ◽  
Dynamical Behaviors ◽  
Positive And Negative Feedback ◽  
The Stability

In this paper, we investigate the complex dynamical behaviors of a biological network that is derived from innate immune responses and that couples positive and negative feedback loops. The stability conditions of the non-negative equilibrium points (EPs) of the system are obtained, using the theory of dynamical systems, and we deduce that no more than three stable EPs exist in this system. Through bifurcation analysis and numerical simulations, we find that the system presents rich dynamical behaviors, such as monostability, bistability and oscillations. These results reveal how positive and negative feedback cooperatively regulate the dynamical behavior of the system.

scholarly journals Stability, Global Dynamics, and Social Welfare of a Two-Stage Game under R&D Spillovers

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Wei Zhou ◽  
Tong Chu ◽  
Xiao-Xue Wang
Keyword(s):  
Social Welfare ◽  
Basin Of Attraction ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Two Stage ◽  
Homogeneous Product ◽  
The Social ◽  
The Stability ◽  
The Given ◽  
D Investment

In this paper, a repeated two-stage oligopoly game where two boundedly rational firms produce homogeneous product and apply gradient adjustment mechanism to decide their individual R&D investment is considered. Results concerning the equilibrium in the built model and the stability are discussed. The effects of system parameters on the complex dynamical behaviors of the built game are analyzed. We find that the system can lose stability through a flip bifurcation or a Neimark–Sacker bifurcation. In addition, the coexistence of multiattractors is also discussed using the so-called basin of attraction. At the end of this research, the social welfare of the given duopoly game is also studied.

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