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Internet evolves into the huge network with new nodes inserted or deleted depending on specific situations. A new model of network topology is needed in order to analyze time-varying internet more realistically and effectively. In this study the non-monotony models are proposed which can describe topological changes of internet such as node insertion and deletion, and can be used for predicting its future topology. Simulation is performed to analyze the topology generated by our model. Simulation results show that our proposed model conform the power law of realistic internet better than conventional ones. The non-monotony model can be utilized for designing internet protocols and networks with better security.