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A model and the stability analysis are proposed for a class of dynamical systems which is difficult in modeling due to the complex physicochemical change by data-driven method. A CARMA cell mapping model is established, whose parameters are identificated by quantum-behaved particle swarm optimization. To avoid the premature convergence of the IQPSO algorithm, the particles position are updated and accurate search capacity is enhanced by applying the neural networks that train the optimal value as the initial weighted value. Based on the model, the stability performance is analyzed by cell mapping theory and dynamic optimization principle, which is helpful to find the whole periodic cell and attractive domain. Simulation studies are included to demonstrate the effectiveness of the proposed approach.