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A novel dynamic-based semi-blind approach is proposed to identify an autoregressive and moving average (ARMA) system in this paper. By using a chaotic driving signal, an ARMA system can be identified accurately by a dynamic-based estimation method called the ergodic-based minimum phase space volume (EMPSV). A maximum-likelihood formulation of EMPSV is provided to certify its unbiasedness and asymptotical efficiency. Monte Carlo simulations show that the EMPSV approach has a smaller mean-square error performance than the minimum phase space volume method and the conventional identification approach based on least-squares estimation with white Gaussian probing signals. The proposed approach is then applied to blind deconvolution of real audio signals and semi-blind channel equalization for chaos communications. It is shown that the EMPSV approach has improved deconvolution and equalization performances compared to conventional techniques in both applications.