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.

Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

2019 ◽  
Vol 20 (2) ◽  
pp. 125-136
Author(s):  
A. M. Yousef ◽  
S. Z. Rida ◽  
Y. Gh. Gouda ◽  
A. S. Zaki
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Theoretical Results

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

scholarly journals Dynamical Analysis of a Stochastic Multispecies Turbidostat Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Yu Mu ◽  
Zuxiong Li ◽  
Huili Xiang ◽  
Hailing Wang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Dilution Rate ◽  
Stochastic Analysis ◽  
Competitive Exclusion ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Stochastic Disturbance ◽  
Dynamical Behaviors ◽  
Theoretical Results

A stochastic turbidostat system in which the dilution rate is subject to white noise is investigated in this paper. First of all, sufficient conditions of the competitive exclusion among microorganisms are obtained by employing the techniques of stochastic analysis. Furthermore, the results demonstrate that the competition among microorganisms and stochastic disturbance will affect the dynamical behaviors of microorganisms. Finally, the theoretical results obtained in this contribution are illustrated by numerical simulations.

Dynamical Study of Competition Cournot-like Duopoly Games Incorporating Fractional Order Derivatives and Seasonal Influences

2020 ◽  
Vol 21 (3-4) ◽  
pp. 339-359
Author(s):  
Abdulrahman Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Economic Systems ◽  
Cournot Duopoly ◽  
Dynamical Study ◽  
Nash Equilibrium Points ◽  
Time Varying Parameters ◽  
Memory Characteristics

AbstractCournot’s game is one of the most distinguished and influential economic models. However, the classical integer order derivatives utilized in Cournot’s game lack the efficiency to simulate the significant memory characteristics observed in many economic systems. This work aims at introducing a dynamical study of a more realistic proposed competition Cournot-like duopoly game having fractional order derivatives. Sufficient conditions for existence and uniqueness of the new model’s solution are obtained. The existence and local stability analysis of Nash equilibrium points along with other equilibrium points are examined. Some aspects of global stability analysis are treated. More significantly, the effects of seasonal periodic perturbations of parameters values are also explored. The multiscale fuzzy entropy measurements for complexity are employed for this case. Numerical simulations are presented in order to verify the analytical results. It is observed that the time-varying parameters induce very complicated dynamics in perturbed Cournot duopoly game compared with the unperturbed game.

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.

scholarly journals Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Noor S. Sh. Barhoom ◽  
Sadiq Al-Nassir
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Predator Species ◽  
Dynamical Behaviors ◽  
Proposed Model ◽  
Constant Rate ◽  
Predator Model ◽  
Theoretical Results

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.

scholarly journals Dynamical analysis of a fractional-order avian-human influenza epidemic model with logistic growth for avian population

2020 ◽  
Vol 14 ◽  
pp. 174830262096670
Author(s):  
Xingyang Ye ◽  
Shimin Lin ◽  
Chuanju Xu
Keyword(s):  
Equilibrium Point ◽  
Fractional Order ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Logistic Growth ◽  
Influenza Epidemic ◽  
Human Influenza

In this paper, a fractional order avian-human influenza epidemic model with logistic growth for avian population is investigated. The dynamical behavior of this model is discussed. We first establish the existence, uniqueness, non-negativity and positive invariance of the solution. Then we analyze the existence of various equilibrium points, and some sufficient conditions are derived to ensure the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, we take some numerical simulations to validate the analytical results.

scholarly journals Multi-stability analysis of fractional-order quaternion-valued neural networks with time delay

2021 ◽  
Vol 7 (3) ◽  
pp. 3603-3629
Author(s):  
S. Kathiresan ◽  
◽  
Ardak Kashkynbayev ◽  
K. Janani ◽  
R. Rakkiyappan ◽  
...  
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Activation Functions ◽  
Geometrical Properties ◽  
Intermediate Value ◽  
Complex Valued ◽  
Theoretical Results

<abstract><p>This paper addresses the problem of multi-stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with time delay. Based on the geometrical properties of activation functions and intermediate value theorem, some conditions are derived for the existence of at least $ (2\mathcal{K}_p^R+1)^n, (2\mathcal{K}_p^I+1)^n, (2\mathcal{K}_p^J+1)^n, (2\mathcal{K}_p^K+1)^n $ equilibrium points, in which $ [(\mathcal{K}_p^R+1)]^n, [(\mathcal{K}_p^I+1)]^n, [(\mathcal{K}_p^J+1)]^n, [(\mathcal{K}_p^K+1)]^n $ of them are uniformly stable while the other equilibrium points become unstable. Thus the developed results show that the QVNNs can have more generalized properties than the real-valued neural networks (RVNNs) or complex-valued neural networks (CVNNs). Finally, two simulation results are given to illustrate the effectiveness and validity of our obtained theoretical results.</p></abstract>

Modeling and stability analysis of the spread of novel coronavirus disease COVID-19

2021 ◽  
pp. 2150035
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
D. Abraham Vianny ◽  
Mary Jacintha ◽  
Fatma Bozkurt Yousef
Keyword(s):  
Fractional Order ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Basic Reproductive Number ◽  
Phase Portraits ◽  
Transmission Model ◽  
Reproductive Number ◽  
Discrete Version ◽  
Novel Coronavirus

Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

scholarly journals A Nonvolatile Fractional Order Memristor Model and its Complex Dynamics

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 955 ◽  
Author(s):  
Wu ◽  
Wang ◽  
Iu ◽  
Shen ◽  
Zhou
Keyword(s):  
Fractional Order ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Stable State ◽  
Electrical Characteristics ◽  
Chaotic Circuit ◽  
Stable States ◽  
Road Map ◽  
Chaotic Circuits ◽  
Integral Order

It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical characteristics of the memristor via Power-Off Plot and Dynamic Road Map. We find that the fractional order memristor has continually stable states and is therefore nonvolatile. We also show that the memristor can be switched from one stable state to another under the excitation of appropriate voltage pulse. The volt–ampere hysteretic curves, frequency characteristics, and active characteristics of integral order and fractional order memristors are compared and analyzed. Based on the fractional order memristor and fractional order capacitor and inductor, we construct a chaotic circuit, of which the dynamic characteristics with respect to memristor’s parameters, fractional order α, and initial values are analyzed. The chaotic circuit has an infinite number of equilibrium points with multi-stability and exhibits coexisting bifurcations and coexisting attractors. Finally, the fractional order memristor-based chaotic circuit is verified by circuit simulations and DSP experiments.

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

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