环形供应链网络中周期性库存振荡的全局分岔与对称性
Global Bifurcation and Symmetry of Periodic Inventory Oscillations in Ring Supply-Chain Networks
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中文总结 AI 辅助
本文针对延迟环形供应链网络，通过等变度理论等方法，研究了周期性库存振荡的全局分岔与对称性，构建了统一分析框架并给出稳定性准则。
中文摘要 AI 辅助
本文研究由相同仓库构成的延迟环形供应链网络中的周期性库存振荡。在将库存-补货系统约化为二阶延迟方程后，我们将周期问题表述为恒等映射的等变紧扰动，其对称性由环形结构、奇数非线性项和时间平移生成。利用等变度理论，我们刻画了临界参数对，计算了相关交叉数，并构造了一个局部分岔不变量，其非零性保证了非常数周期解的存在，并提供其空间及时空对称类型的信息。通过将双参数问题限制在可允许横截曲线上，我们进一步建立了分岔分支的全局延续择一性。具有\boldsymbol{D_7}和\boldsymbol{D_8}对称性的示例说明了临界参数、分岔不变量和可允许轨道类型的计算。最后，将弗洛凯（Floquet）理论应用于小振幅周期分支，得到了非共振扰动模式的 leading-order（首阶）稳定性准则。这些结果为描述延迟环形供应链网络中周期性库存振荡的存在性、对称性、全局延续性及首阶稳定性提供了统一框架。
英文摘要
This paper studies periodic inventory oscillations in delayed supply-chain networks of identical warehouses arranged in a ring. After reducing the inventory--replenishment system to a second-order delay equation, we formulate the periodic problem as an equivariant compact perturbation of the identity, with symmetries generated by the ring structure, the odd nonlinearity, and time translations. Using equivariant degree theory, we characterize critical parameter pairs, compute the associated crossing numbers, and construct a local bifurcation invariant whose nonvanishing guarantees nonconstant periodic solutions and provides information about their spatial and spatio-temporal symmetry types. By restricting the two-parameter problem to an admissible transversal curve, we further establish a global continuation alternative for the bifurcating branches. Examples with \(D_7\)- and \(D_8\)-symmetry illustrate the computation of critical parameters, bifurcation invariants, and admissible orbit types. Finally, Floquet theory is applied to small-amplitude periodic branches, yielding a leading-order stability criterion for nonresonant perturbation modes. The results provide a unified framework for describing the existence, symmetry, global continuation, and leading-order stability of periodic inventory oscillations in delayed ring supply-chain networks.
