The development of COVID-19 vaccine is highly concerned by all countries in the world. So far, many kinds of COVID-19 vaccines have entered phase III clinical trial. However, it is difficult to deliver COVID-19 vaccines efficiently and safely to the areas affected by the epidemic. This paper focuses on vaccine transportation in a supply chain model composed of one distributor and one retailer (clinic or hospital), in which the distributor procures COVID-19 vaccines from the manufacturer and then resells them to the retailer. Distributor detects the activity level of the vaccines, and retailer is responsible for transportation of the vaccines. Firstly, we establish a difference equations model with time-delay. Secondly, we investigate the impact of time-delay on the stability of vaccine supply chain. In addition, we explore the influence of decision adjustment speed of the distributor (or retailer) on the stability of vaccine supply chain. Finally, we verify the theoretical results by a two-dimensional bifurcation diagram, the largest Lyapunov exponent, entropy, and domain of attraction. The results show that when the decision delay-time or the adjustment speed of decision variables exceeds a certain threshold, it brings a negative impact on the stability of vaccine supply chain system. The stability domain of the system shrinks as customers’ sensitivity to cold chain transportation decreases and by contrast expends as customers’ sensitivity to vaccine prices decreases. When the vaccine supply chain is in a state of chaos, the effect of external control over the system is superior to that of internal control over the system.

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.

Purpose: The purpose of this study is to analyze the short-term development pattern and long-term development trend of the digital supply chain.Design/methodology/approach: This study uses the combination of short-term game and long-term evolutionary game theory.Findings: Findings of this study suggest that irrational decisions can make the evolutionary path of the digital supply chain complex and unpredictable.Originality/value: This study proposes an evolutionary game model for the digital supply chain that can provide good guidance for the digitalization process of enterprises.

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.

Due to the important role of the vaccines in the prevention of global epidemics, this paper focuses on a vaccine transportation supply chain composed of one distributor and one retailer. Based on the assumption that the decision-maker does not make a decision instantaneously, we present a decision-making time-delay model. Firstly, we captured some sufficient conditions of delay-induced bifurcation for the model by regarding different combinations of the decision delay periods as the bifurcation parameters and analyzed how the speed of decision-making adjustment of distributor or retailer affects the critical point of system stability. Secondly, we made a numerical simulation on the model by using a two-dimensional bifurcation diagram, largest Lyapunov exponent, and entropy and chaotic attractor, respectively. Finally, we used two coordination methods to control chaos and compared them. The results show that when the decision delay exceeds a certain threshold, the system will lose stability or go into chaos. The precipitous speed of decision variable adjustment of the distributor or retailer will increase the entropy of the system and lead the system into a chaotic state. When the vaccine supply chain is in chaos, the effect of external control on chaos is better than that of internal control on chaos.