Notations.

In this study, the dynamic effects of new product supply chain cooperation behavior on optimal government subsidies and supply chain decision-making are studied by establishing a nonlinear discrete inventory decision system; In this system, the government subsidizes authorized remanufacturers to promote remanufacturing, and cooperative behavior exists in the supply chain of new products. The research method is modeling and simulation of a supply chain system based on nonlinear system dynamics theory. The complexity analysis includes the stability analysis of the decision system, the path of the system into chaos, the change of entropy of the system and the performance in chaos system. Our findings indicate that the optimal government subsidy in the cooperative model is lower than that in the non-cooperative model. Consumer surplus is the main reason for the subsidy difference between the two models. In comparison with the cooperative supply chain, the stability of the non-cooperative supply chain is more easily affected by government subsidies. Further, the market is more likely to enter chaos due to improper adjustment of the new products’ inventory with cooperative behavior in the supply chain of new products. When the system enters chaos, the new product supply chain’s profit in the cooperative system is more likely to be far lower than the equilibrium profit. This study provides a theoretical reference for supply chain inventory management and government subsidy remanufacturer decision-making from the perspective of dynamic systems science.</div

The impact <i>α</i>₂ and <i>α</i>₃ on average profits of supply chain.

The impact α2 and α3 on average profits of supply chain.</p

The impact of <i>α</i>₄ on average profits of supply chain.

The impact of α4 on average profits of supply chain.</p

Influence of <i>α</i>₃ on multi-cycle decision-making.

(a) Bifurcation diagram with α3 in model N. (b) Bifurcation diagram with α3 in model C. (c) Time series of qn with α3 = 8.7 in model N and α3 = 5.3 in model C.</p

Social welfare variation with government subsidies.

Social welfare variation with government subsidies.</p

Influence of <i>α</i>₂ on multi-cycle decision-making.

(a) Bifurcation diagram with α2 in model N. (b) Bifurcation diagram with α2 in model C. (c) The system’s entropy with varying α2.</p

Impact of government subsidies.

(a) The consumer surplus vary with the subsidy. (b) Carbon taxes vary with subsidies. (c) Effect of government subsidies on subsidy costs. (d) Effect of government subsidies on supply chain profits.</p

Influence of <i>α</i>₄ on multi-cycle decision-making.

(a) Bifurcation diagram with α4. (b) The largest Lyapunov exponent with α4.</p

Fig 10 -

Diagram of attractor: (a) model N with α2 = 4.5 and α3 = 7.8. (b) Model C with α2 = 6.4 and α3 = 5.5.</p

S1 File -

In this study, the dynamic effects of new product supply chain cooperation behavior on optimal government subsidies and supply chain decision-making are studied by establishing a nonlinear discrete inventory decision system; In this system, the government subsidizes authorized remanufacturers to promote remanufacturing, and cooperative behavior exists in the supply chain of new products. The research method is modeling and simulation of a supply chain system based on nonlinear system dynamics theory. The complexity analysis includes the stability analysis of the decision system, the path of the system into chaos, the change of entropy of the system and the performance in chaos system. Our findings indicate that the optimal government subsidy in the cooperative model is lower than that in the non-cooperative model. Consumer surplus is the main reason for the subsidy difference between the two models. In comparison with the cooperative supply chain, the stability of the non-cooperative supply chain is more easily affected by government subsidies. Further, the market is more likely to enter chaos due to improper adjustment of the new products’ inventory with cooperative behavior in the supply chain of new products. When the system enters chaos, the new product supply chain’s profit in the cooperative system is more likely to be far lower than the equilibrium profit. This study provides a theoretical reference for supply chain inventory management and government subsidy remanufacturer decision-making from the perspective of dynamic systems science.</div