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In this study, we investigate a class of Fast Transmission Control Protocol (FAST TCP) network with a delayed state feedback mechanism in terms of nonlinear dynamics, including local stability and periodic bifurcation. First, we successfully addressed the local stability of the system by employing the $\tau $ -decomposition strategy and provided an explicit expression for the delay stability interval. Second, we apply the normal form theory and the central manifold theorem to study the bifurcation solutions in depth and clarify the direction of the Hopf bifurcation as well as the stability of the bifurcation periodic solutions. In addition, the explicit bifurcation parameters are intuitively given by us using a symbolic arithmetic tools. Finally, by presenting a numerical example, we verify the accuracy of the theoretical analysis and demonstrate that the method is highly accurate and effective. These findings provide important theoretical support for deepening the understanding of the dynamic properties of time-lagged state feedback mechanisms in FAST TCP networks and the optimization of network control systems.

Since financing issues of research and development (R&D) directly determine the success of green supply chain initiatives, the choice of funding mechanisms becomes key for green supply chain participants. However, there are few quantitative studies on the financing issues of green supply chains. We study green R&D financing issues for a two-echelon green supply chain, in which a green manufacturer and a regular manufacturer produce and sell green and regular products to a retailer, respectively. External and internal funding mechanisms as well as consumer green loyalty are considered in this study, which encourages green manufacturers to produce environment-friendly products. Three game models, namely, a partially centralized system, government subsidy, and two-part tariff contract scenarios, are formulated to investigate green R&D financing issues. The analytical results show that: (a) Government subsidies cannot effectively promote green manufacturers to improve the greenness of products if the amount of the government subsidy does not exceed a threshold. (b) Under government subsidy schemes, with an increase in subsidies, the output of green products first reaches the level under the partially centralized system, followed by the greenness of products. (c) The two-part tariff contract with a reasonable fixed fee can effectively coordinate retailers and green manufacturers to achieve cooperation, in which the greenness level of products and the retail price are equal to the values under the partially centralized system. (d) Retailers and green manufacturers have different preferences of financing modes; two-part tariff contracts are favored by retailers, while government subsidies are preferred by green manufacturers.

There is a general agreement in the brain computer interface community that the feature extracting method called the common spatial pattern (CSP) combined with nonlinear classifiers can provide excellent results in some cases. However, CSP is also known to be very sensitive to noise and prone to over fitting, and the performance of this spatial filter is closely related to the operational frequency band of electroencephalogram data. To address this issue, we propose a new method FB-TRCSP+RF based on CSP and random forest. The FB-TRCSP is combined by the 8th-order Butterworth bandpass-filters and the CSP with Tikhonov regularization, which is a more robust feature extraction method compared to the CSP. Then, the model is applied to an experimental data set collected from 14 subjects and is compared with the non-regularization method FB-CSP+RF. The results show that the method we proposed yields relatively higher median classification accuracies and shows a stronger ability in subject-to-subject learning compared to prevailing approaches.