In this paper, an output dynamic game model of intertwined supply chains operating in two different countries is established. The Nash equilibrium point of the model and its stable region are obtained using nonlinear dynamic principles. The complex properties of the system, such as stability, period-doubling bifurcations, and chaos, are investigated using numerical simulations. Our results suggest that the level of output and the system’s profits undergo bifurcation and chaos with an increase in the output adjustment speed. An interesting phenomenon occurs in that higher tariffs lead to the expansion of the stable range of the supply chain in the product-exporting country. The chaotic behavior of the system is sensitive to the value of the initial level of output. In supply chain competition, each supply chain firm should make suitable adjustments to the speed of output. To maintain the stability of domestic markets, excessive tariffs should be avoided. It is essential that each supply chain firm evaluates the potential impacts of different initial output values when making initial decisions. Using the method of delayed feedback control, the chaotic behavior of the system can effectively be controlled. These findings offer valuable and novel insight into inter-chain competition in supply chain networks.

To investigate the dynamic complexity of chain-to-chain output decisions in a closed-loop supply chain system of cross-border e-commerce (CBEC), this study decomposes the system into four product–market (PM) chains, based on the e-commerce platform’s information-sharing strategy and the manufacturer’s selected logistics mode (direct mail or bonded warehouse). By combining game theory with complex systems theory, discrete dynamic models for output competition among PM chains under four scenarios are constructed. The Nash equilibrium solution and stability conditions of the models are derived according to the principles of nonlinear dynamics. The stability of the model under the four scenarios, as well as the impacts of the initial output level and comprehensive tax rates on the stability and stability control of the system, are analyzed using numerical simulation methods. Our findings suggest that maintaining system stability requires controlling the initial output levels, the output adjustment speeds, and tariff rates to remain within specific thresholds. When these thresholds are exceeded, the entropy value of the model increases, and the system outputs decisions to enter a chaotic or uncontrollable state via period-doubling bifurcations. When the output adjustment speed of the four PM chains is high, the direct-mail logistics mode exhibits greater stability. Furthermore, under increased tariff rates for CBEC, the bonded warehouse mode has a stronger ability to maintain stability in system output decisions. Conversely, when the general import tax rate increases, the direct-mail mode demonstrates better stability. Regardless of the logistics mode, the information-sharing strategy can enhance the stability of system output decisions, while increased e-commerce platform commission rates tend to reduce stability. Interestingly, the use of a non-information-sharing strategy and the direct-mail logistics mode may be more conducive to increasing the profit levels of overseas manufacturers. Finally, the delayed feedback control method can effectively reduce the entropy value, suppress chaotic phenomena in the system, and restore stability to output decisions from a fluctuating state.

To investigate the impact of recycling modes on the stability of cross-border supply chain (SC) systems, this paper decomposes a cross-border SC system, consisting of two countries with different recycling capabilities for electronic products, such as Singapore and Vietnam, into three product-market chains (PMCs). Discrete dynamical models for output and recycling rate decisions of the system are developed based on four recycling modes. The Nash equilibrium solutions and stability conditions of the models are obtained via nonlinear dynamics principles; the stable regions and chaotic phenomena of the system, and the impact of tariff on the system stability are investigated through numerical simulation. Our findings suggest that to ensure the system stability, PMCs should adjust output and recycling rates, respectively, at low speeds. Retailer recycling mode shows the largest stable region of system decisions. When the adjustment speeds of output and recycling rate increase, the stable regions of the system in the four recycling modes are compacted. In addition, an increase in tariff levels can adversely affect the system stability. Finally, increasing recycling prices and marginal recycling transaction costs can expand the stable regions of the system, mitigate the adverse impact of tariffs, and enhance the profit stability of the closed-loop PMC.