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FAST TCP is a newly developed transfer control protocol for future networks with high bandwidth delay product. At present, analyzing the stability of FAST TCP in different networks is an active research area. We establish a group of nonlinear delay differential equations to describe the window adjustment algorithm of FAST TCP and the queuing behavior of routers in single-link multi-source networks. Based on the model of the system, we further derive a sufficient condition for local stability of the system, which is decoupled from the network conditions. The conclusion presented here is fully verified by extensive simulations.