Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization

Li, Hui; Zhou, Wei; Elsadany, A. A.; Chu, Tong

doi:10.1016/j.chaos.2021.110936

Cited by 28 publications

(5 citation statements)

References 47 publications

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“…The necessary and sufficient conditions for the stability of the extended observer based on the Jury criterion are as follows 36 : Substitute the values of p 0, p 1 and p 2 into the above equation to obtain: Therefore, in order to ensure the stability of the decoupled extended state observer, the constraints of Equation (48) above must be met when selecting the parameters of the decoupled extended state observer，usually, the gain parameter β 1, β 2 of the decoupled expansion observer is greater than 0, the sampling period T s is also greater than 0. So based on the selection conditions of β 1, β 2, and T s, Equation (48) can be simplified as follows: Solving inequality in Equation (49) can obtain: The bandwidth method is generally used for parameter selection for extended observers, namely β 1 = 2 ω o, β 2 = ω o 2.…”

Section: Methodsmentioning

confidence: 99%

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Research on the control strategy of LCL grid-connected inverters based on improved auto disturbance rejection

Han,

Xu,

Kang

et al. 2023

Science Progress

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The grid-connected inverter is the key to ensure stable, reliable, safe, and efficient operation of the power generation system; the quality of the grid-connected output current waveform directly affects the performance of the entire power generation system. To improve the anti-interference performance and reduce the output current harmonic content of the grid-connected inverter, an improved control strategy that combined repetitive control (RC) and auto disturbance rejection control (ADRC) is designed in this paper. Firstly, decoupled the ADRC to realize the individual adaptation between tracking performance parameters and anti-interference performance parameters of the controller, through which the difficulty of adjusting parameters is reduced. Secondly, the control approach is devised by adding RC to ADRC. To demonstrate the effectiveness of the proposed method in this paper, detailed experimental studies are conducted using proportional integral control, traditional ADRC, and the proposed method under normal power grids, weak power grids, and periodic disturbances. And dynamic performance simulation experiment is done to verify the dynamic performance of the self-disturbance rejection controller before and after the addition of RC links. The results indicated the effectiveness and feasibility of the proposed method. Finally, after simulation, the steady state and dynamic performance are conducted on a hardware testing platform. The impacts of the obtained results indicate the effectiveness and feasibility of the control algorithm proposed, the ability to suppress intermediate frequency disturbances is improved, the bandwidth of the auto disturbance rejection controller is expanded, and the harmonic content of the output current is depressed.

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Section: Methodsmentioning

confidence: 99%

“…The necessary and sufficient conditions for the stability of the extended observer based on the Jury criterion are as follows 36 :…”

Section: Stability Analysis Of Rc-adrc Decoupling Extended Observermentioning

confidence: 99%

Research on the control strategy of LCL grid-connected inverters based on improved auto disturbance rejection

Han,

Xu,

Kang

et al. 2023

Science Progress

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“…Te Lyapunov stability (hereafter, L-stability) at a fxed point was formally defned by Clark Robinson in 2012 [2] for a state description of diferential equation solutions of being close to an equilibrium point. In the following years, this concept emerged in various studies, and these studies mainly focused on diferent types of systems, for example, topologic dynamical systems, diferential systems, neural network systems, and epidemiology systems (see References [3][4][5][6]). However, there is limited evidence of the nature and characterization of L-stability at a point in the literature.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov Stability in the Cournot Duopoly Game

Zhu

2023

Discrete Dynamics in Nature and Society

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This paper studies Lyapunov stability at a point and its application in the Cournot duopoly game. We first explore the relationship between Lyapunov stability at a point, nonsensitivity and non-Devaney chaos and find that a dynamical system is nonsensitive and non-Devaney chaotic if there is a point in this system such that it is Lyapunov stable at that point. We next prove a group of equivalent characterizations of Lyapunov stability at a point to deduce the composite theorems and product theorems of Lyapunov stability at a point, and then we prove three equivalent characterizations of the Cournot duopoly system to demonstrate that this system is Lyapunov stable at its unique nonzero fixed point (Cournot equilibrium point) when the unit costs of the Cournot double oligarchies satisfy certain conditions. Therefore, we conclude that the Cournot duopoly system is safe relative to both sensitivity and Devaney chaos. The robustness of our results are also verified by conducting numerical simulations in the Cournot duopoly game.

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“…Askar and Al-khedhairi [6] implemented concrete discussion on local and global stability of the equilibrium points for a duopoly game concerning price competition. For more detailed works on this aspect, one can see the literature [7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

et al. 2023

Fractal Fract

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In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier publications, we propose a new fractional-order Bertrand duopoly game model incorporating both nonidentical time delays. The dynamics involving existence and uniqueness, non-negativeness, and boundedness of solution to the considered fractional-order Bertrand duopoly game model are systematacially analyzed via the Banach fixed point theorem, mathematical analysis technique, and construction of an appropriate function. Making use of different delays as bifurcation parameters, several sets of new stability and bifurcation conditions ensuring the stability and the creation of Hopf bifurcation of the established fractional-order Bertrand duopoly game model are acquired. By virtue of a proper definite function, we set up a new sufficient condition that ensures globally asymptotically stability of the considered fractional-order Bertrand duopoly game model. The work reveals the impact of different types of delays on the stability and Hopf bifurcation of the proposed fractional-order Bertrand duopoly game model. The study shows that we can adjust the delay to achieve price balance of different products. To confirm the validity of the derived criteria, we put computer simulation into effect. The derived conclusions in this article are wholly new and have great theoretical value in administering companies.

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Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization

Cited by 28 publications

References 47 publications

Research on the control strategy of LCL grid-connected inverters based on improved auto disturbance rejection

Research on the control strategy of LCL grid-connected inverters based on improved auto disturbance rejection

Lyapunov Stability in the Cournot Duopoly Game

Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

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