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By introducing the logistic-like technology, the classical Solow-Swan model is extended to inquire the technological overflow and catch-up of the developing economy in this paper. The improved model is described by a two-dimensional dynamical system. It is proved that the model has a unique equilibrium which is a sink and the solution of the equation is globally asymptotically stable. And the classical Solow-Swan model is a special case of the model given here. The economic growth patterns are discussed by phase portrait analysis at the end of this paper.