| Citation: |
Hongyan Sun, Shuhuan Tian, Jianzhi Cao, Pengmiao Hao. STABILITY AND BIFURCATION OF A NEUTRAL-TYPE DELAY DIFFERENTIAL GAME SYSTEM IN GREEN SUPPLY CHAINS: A GLOBAL SENSITIVITY ANALYSIS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2668-2704. doi: 10.11948/20250326
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STABILITY AND BIFURCATION OF A NEUTRAL-TYPE DELAY DIFFERENTIAL GAME SYSTEM IN GREEN SUPPLY CHAINS: A GLOBAL SENSITIVITY ANALYSIS
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Abstract
This paper investigates a two-echelon dual-channel green supply chain via a neutral delay differential game model, focusing on supply chain coordination and system stability analysis. We compare equilibrium outcomes under centralized and decentralized decision-making, propose a transfer payment mechanism for coordination, and explore stability properties using eigenvalue methods, Sobol global sensitivity analysis, and numerical simulations. Results show that centralized decision-making outperforms decentralized decision-making in green technology level and total supply chain profit, while the transfer payment mechanism achieves Pareto improvements within a specific parameter range. Stability analysis identifies the discount rate, consumer green sensitivity, and price weight coefficient as dominant stability determinants: The price weight coefficient acts as a critical stability switch inducing Hopf bifurcation, and the discount rate extended to the real number domain directly determines equilibrium stability type. Simulations visualize stability regions and oscillation behaviors, while global sensitivity analysis quantifies parameter influences, confirming the discount rate and consumer green sensitivity as the most impactful factors. Numerical simulations further verify the theoretical findings and establish a clear link between parameter sensitivity and system stability.
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References
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Hongyan Sun, Shuhuan Tian, Jianzhi Cao, Pengmiao Hao. STABILITY AND BIFURCATION OF A NEUTRAL-TYPE DELAY DIFFERENTIAL GAME SYSTEM IN GREEN SUPPLY CHAINS: A GLOBAL SENSITIVITY ANALYSIS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2668-2704. doi: 10.11948/20250326
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Figure 1.
Global sensitivity analysis of key parameters in the dual channel green supply chain.
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Figure 2.
The influence of
$ \rho $ $ g_{1}^{*} $ $ \rho $ $ g_{2}^{*} $ -
Figure 3.
The 3D visual graphs of the global sensitivity analysis results.
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Figure 4.
Local stability of the equilibrium
$ E_{1} $ -
Figure 5.
Change of stability for
$ E_{1} $ $ \theta $ -
Figure 6.
Stability regions in the
$ \rho $ $ a_2 $ $ \theta=0.6 $ $ \tau=5 $ $ G_{3} $ -
Figure 7.
Oscillation amplitude versus
$ \theta $ $ \tau $ $ G_{3} $