Complex Dynamics of a Continuous Bertrand Duopoly Game Model with Two-Stage Delay

Ma, Junhai; Si, Fengshan

doi:10.3390/e18070266

Cited by 49 publications

(32 citation statements)

References 24 publications

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“…There are some researches who connected entropy with management and economics. In Ma and Si [16] research, entropy was used to predict the financial time series; they drew the conclusion that financial forecasts of foreign exchange currency in low entropy regions have a slight advantage in trading, and it is very difficult to achieve the predicting time series in high entropy regions. Han et al [17] established a hydropower duopoly game with two time delays and analyzed the influence of delay parameter on the entropy and dynamic features of the system.…”

Section: Introductionmentioning

confidence: 99%

Research on the Complexity and Chaos Control about a Closed‐Loop Supply Chain with Dual‐Channel Recycling and Uncertain Consumer Perception

Ren

et al. 2018

Complexity

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According to game theory, chaotic dynamics theory, and complexity based on the literature review about the pricing strategy and recycling channels of the closed-loop supply chain, on the background of the widespread hybrid recycling channels in Chinese electronic products market, this paper builds a closed-loop supply chain model with dual-channel recycling composed of one manufacturer and one third-party. We assume that the consumer perception towards the remanufacturing products is uncertain and limited. We carry on theoretical analysis of this model and perform numerical simulations from the perspective of entropy theory. Results show that a precipitous speed of recycling price adjustment of the manufacturer or the third-party will both lead the system into a chaotic state and cause the entropy of the system to increase. The system is sensitive to initial conditions in this chaotic condition. Focusing on the harmful effects of chaotic system, we introduce adjustment parameter to efficiently control the chaos. The results have a strong reference value to practical problems, so it has a great value in both theory and application.

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Section: Introductionmentioning

confidence: 99%

Research on the Complexity and Chaos Control about a Closed‐Loop Supply Chain with Dual‐Channel Recycling and Uncertain Consumer Perception

Ren

et al. 2018

Complexity

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“…Song and Zhao [13] pointed out a decisionmaking problem of newsvendor system with strategic customers of bounded rationality. Ma and Si [14] established a continuous Bertrand duopoly game model with twostage delay to investigate the influence of delay and weight on the complex dynamic characteristics of the system. Ma and Xie [15] analyzed the comparison and complexity on a dual-channel supply chain under the different channel power structures and uncertain demand.…”

Section: Introductionmentioning

confidence: 99%

Research on Supply Chain Stability Driven by Consumer’s Channel Preference Based on Complexity Theory

Tian

Lou

2018

Complexity

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At present, most of the manufacturers are increasingly laying emphasis on dual-channel selling. The level of consumer's preference is diverse with different channels. This study discusses a supply chain where one common manufacturer uses two different channels to sell product. The bounded rationality expectation has been applied to explore the decision-making mechanism in finalizing the wholesale prices and sales commissions for the manufacturer and retailers. In addition, the dynamic features of the system are simulated by 2D bifurcation diagram, the largest Lyapunov exponent, attractor variation, and time series. The simulation results suggest that if the adjustment speeds of the wholesale prices and sales commissions change drastically, the system would fall into a chaotic state. If the consumers prefer the online channel, the wholesale prices and sales commissions may be raised and vice versa. However, too strong preference of each channel will make the system appear to have a considerably periodic fluctuation, even chaos. In the meantime, the parameter adjustment method can help make the periodic or chaotic system go back to stability. Therefore, the significance of this study is with a practical meaning to make better pricing strategy for players in dual-channel selling supply chain system.

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“…For simplicity, the linear form of Model (2) at the equilibrium point E(x * , y * , z * , w * ) through the Jacobian matrix is as follows [18]:…”

Section: Local Stability and The Existence Of Hopf Bifurcationmentioning

confidence: 99%

Entropy and Stability Analysis of Delayed Energy Supply–Demand Model

Wang

et al. 2016

Entropy

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Abstract:In this paper, a four-dimensional model of energy supply-demand with two-delay is built. The interactions among energy demand of east China, energy supply of west China and the utilization of renewable energy in east China are delayed in this model. We discuss stability of the system affected by parameters and the existence of Hopf bifurcation at the equilibrium point from two aspects: single delay and two-delay. The stability and complexity of the system are demonstrated through bifurcation diagram, Poincare section plot, entropy diagram, etc. in numerical simulation. The simulation results show that the parameters beyond the stable region will cause the system to be unstable and increase the complexity of the system. At this point, because of energy supply-demand system fluctuations, it is difficult to formulate energy policies. Finally, the bifurcation control is realized successfully by the method of delayed feedback control. The results of bifurcation control simulation indicate that the system can return to stable state by adjusting the control parameter. In addition, we find that the bigger the value of the control parameter, the better the effect of the bifurcation control. The results of this paper can provide help for maintaining the stability of the system, which will be conducive to energy scheduling.

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Complex Dynamics of a Continuous Bertrand Duopoly Game Model with Two-Stage Delay

Cited by 49 publications

References 24 publications

Research on the Complexity and Chaos Control about a Closed‐Loop Supply Chain with Dual‐Channel Recycling and Uncertain Consumer Perception

Research on the Complexity and Chaos Control about a Closed‐Loop Supply Chain with Dual‐Channel Recycling and Uncertain Consumer Perception

Research on Supply Chain Stability Driven by Consumer’s Channel Preference Based on Complexity Theory

Entropy and Stability Analysis of Delayed Energy Supply–Demand Model

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