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Ethernet has some attractive properties for network consolidation in the data center, but needs further enhancement to satisfy the additional requirements of unified network fabrics. Congestion management is introduced in Ethernet networks to avoid dropping packets due to congestion. The BCN (Backward Congestion Notification) mechanism is a basic element of several standard drafts, and its stability underlies normal network operations. Because the linear stability analysis method is incapable of handling the nonlinearity of the variable structure control employed by the BCN mechanism, some particular phenomena are unexposed and the insights are insufficient. In this paper, we propose the concept of strong stability of the queuing system to satisfy the requirements of no dropped packets in the data center, and build a fluid-flow analytical model for the BCN congestion control system. Considering the nonlinearity involved in the rate regulation laws, we classify the system into different categories according to the shapes of phase trajectories, and conduct a nonlinear stability analysis using phase plane analysis techniques on a case by case basis. The analysis details can provide a comprehensive understanding about the behaviors of the overall congestion control system. Finally, we also deduce an explicit stability criterion presenting the parameters constraints for the strongly stable BCN system, which can provide straightforward guidelines for proper parameter settings.