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The attractor of Model (22) when τ 1 = 0.1 < τ 10 = 0.2208 , τ 2 = 0 : (a) x ( t ) , y ( t ) , z ( t ) ; and (b) x ( t ) , z ( t ) , w ( t ) .
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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 t...
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Citations
... Ma and Si [36] studied the stability of the duopoly price game model in two stages and analyzed the effects of parameters such as delay variables on the stability of the game system. Wang et al. [37] studied the influence of delay decision variables on the stability and complexity of the energy supply and demand system and give the evolutionary trajectory and stability region of the system. ...
... It can be seen that the stability of enterprises in leading position is stronger under the same conditions. e largest Lyapunov exponent diagrams of the system further show that the critical value of price bifurcation of Enterprise 2 is τ 0 � 0.25 in Figure 3(b) [36,37]. Figures 3(a) and 3(c) shows that the more sensitive consumers are to the product price (α increases), the larger the stability region of the system with respect to the delay parameter τ is when other conditions are constant. ...
Taking the carbon emissions per unit product as the standard to measure the low-carbon technology level of the enterprise, this article analyzed how the technology supplier enterprises realize low-carbon production and achieve a win-win situation for both supply and demand through technology sharing through technology research and development. Based on the positive effect of low-carbon technology level on product demand, we studied the optimal pricing strategy and the optimal low-carbon technology level in the technology supply enterprises under the Stackelberg game in 3 conditions (i.e., without technology research and development or technology sharing, with technology research and development but no technology sharing, and with both technology research and development and technology sharing). We also drew a comparative analysis of the optimal product price, the optimal low-carbon technology level, and the optimal profit in the three scenarios. Besides, by constructing a delayed differential price game model, we studied the equilibrium strategy of price competition between technology supply and demand companies and the local asymptotic stability of the game system at the equilibrium point. In addition, the effects of delay strategy on game equilibrium strategy, the influence of the degree of adjustment of decision variables on the stability of the game system, and the stability of the game system on the evolution trend of the game are also explored. By comparing and analyzing the game results of the oligopoly enterprises in the stable system and the unstable system, it confirmed that the system instability usually causes serious harm to the enterprise.
... The performance evaluation of the UEI is inspired from the performance evaluation of the EI, and entropy is used in researches [9,10] to evaluate the overall performance of the systems. Information entropy is used in this research for UEI connects energy to information. ...
... • Put the statistics of probability distribution of each energy supply-demand matching degree as raw data to substitute the definition of information entropy of energy supply-demand matching degree (9), and calculate the evaluation value of distributed energy station "i" corresponding to the information entropy of energy supply-demand matching degree in a certain period "m". ...
This paper studies the performance of UEI (Ubiquitous Energy Internet) by means of its energy supply-demand matching degree. First of all, the energy supply-demand matching degree of UEI is defined, and then the information entropy of energy supply-demand match degree is defined either by use of Shannon's information entropy theory. On the basis of these two definitions, the energy matching degree information entropy of the distributed Energy Internet is defined. By the study of information entropy characteristic and energy supply-demand matching degree, the evaluation model of energy supply-demand matching degree of UEI is provided, and the performance of UEI is evaluated. Finally, the effectiveness of this evaluation model in solving the supply-demand performance evaluation problem of UEI is proved by an example.
... if sin 10 0 ̸ = 0, then Re[ ( 0 )/ ] −1 ̸ = 0. According to the corollary in [21][22][23][24], we have the following conclusions. Theorem 3. If ̸ = 0 and sin 10 0 ̸ = 0, then the equilibrium point ( * ) of (10) is asymptotically stable for ∈ [0, 0 ), and it is unstable when > 0 . ...
A temperature index model with delay and stochastic perturbation is constructed in this paper. It explores the influence of parameters and stochastic factors on the stability and complexity of the model. Based on historical temperature data of four cities of Anhui Province in China, the temperature periodic variation trends of approximately sinusoidal curves of four cities are given, respectively. In addition, we analyze the existence conditions of the local stability of the temperature index model without stochastic term and estimate its parameters by using the same historical data of the four cities, respectively. The numerical simulation results of the four cities are basically consistent with the descriptions of their historical temperature data, which proves that the temperature index model constructed has good fitting degree. It also shows that unreasonable delay parameter can make the model lose stability and improve the complexity. Stochastic factors do not usually change the trend in temperature, but they can cause high frequency fluctuations in the process of temperature evolution. Stability control is successfully realized for unstable systems by the variable feedback control method. The trend of temperature changes in Anhui Province is deduced by analyzing four typical cities.
... Then, we can draw the following conclusions [26,27]: ...
This paper constructs a continuous dual-channel closed-loop supply chain (DCLSC) model with delayed decision under government intervention. The existence conditions of the local stability of the equilibrium point are discussed. We analyze the influence of delay parameters, the adjustment speed of wholesale price, recovery rate of waste products, direct price, carbon quota subsidy, and carbon tax on the stability and complexity of model by using bifurcation diagram, entropy diagram, attractor, and time series diagram and so on. Besides, the delay feedback control method is adopted to control the unstable or chaotic system effectively. The main conclusions of this paper show that the variables mentioned above must be within a reasonable range. Otherwise, the model will lose stability or enter chaos. The government can effectively adjust manufacturers' profit through carbon tax and carbon quota subsidy, and encourage manufacturers to reduce carbon emissions and increase the remanufacturing of waste products.
