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As an emerging non-parametric modeling technique, the methodology of support vector regression blazed a new trail in identifying complex nonlinear systems with superior generalization capability and sparsity. Nevertheless, the conventional quadratic programming support vector regression can easily lead to representation redundancy and expensive computational cost. In this paper, by using the l1 norm minimization and taking account of the different characteristics of autoregression (AR) and the moving average (MA), an innovative nonlinear dynamical system identification approach, linear programming SVM-ARMA2K, is developed to enhance flexibility and secure model sparsity in identifying nonlinear dynamical systems. To demonstrate the potential and practicality of the proposed approach, the proposed strategy is applied to identify a representative dynamical engine model.