The increasing use of synthetic data from the public Internet has enhanced data usage efficiency in large language model (LLM) training. However, the potential threat of model collapse remains insufficiently explored. Existing studies primarily examine model collapse in a single model setting or rely solely on statistical surrogates. In this work, we introduce LLM Web Dynamics (LWD), an efficient framework for investigating model collapse at the network level. By simulating the Internet with a retrieval-augmented generation (RAG) database, we analyze the convergence pattern of model outputs. Furthermore, we provide theoretical guarantees for this convergence by drawing an analogy to interacting Gaussian Mixture Models.