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.

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.

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.

This paper studies the pricing of American carbon emission derivatives and its numerical method under the mixed fractional Brownian motion. To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional Black–Scholes, which is more in line with the actual characteristics of the option market. We have outlined a power penalty approach using parabolic variation inequality and linear complementarity (LCP) which arises from mixed fractional Brownian motion. In addition, we introduced a nonuniform grid-based modification of the fitted finite volume method for numerical solution. Numerically, we show the impact of Hurst exponent on the pricing and analyze the convergence rates of the proposed penalty method. In conclusion, since mfBm is a well-developed mathematical model of strongly correlated stochastic processes, this model will be an efficient model for pricing carbon financial derivative.

In this paper, we build a model of energy-savings and emission-reductions with two delays. In this model, it is assumed that the interaction between energy-savings and emission-reduction and that between carbon emissions and economic growth are delayed. We examine the local stability and the existence of a Hopf bifurcation at the equilibrium point of the system. By employing System Complexity Theory, we also analyze the impact of delays and the feedback control on stability and entropy of the system are analyzed from two aspects: single delay and double delays. In numerical simulation section, we test the theoretical analysis by using means bifurcation diagram, the largest Lyapunov exponent diagrams, attractor, time-domain plot, Poincare section plot, power spectrum, entropy diagram, 3-D surface chart and 4-D graph, the simulation results demonstrating that the inappropriate changes of delays and the feedback control will result in instability and fluctuation of carbon emissions. Finally, the bifurcation control is achieved by using the method of variable feedback control. Hence, we conclude that the greater the value of the control parameter, the better the effect of the bifurcation control. The results will provide for the development of energy-saving and emission-reduction policies.