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This paper focuses on diversity and convergence analysis of the membrane algorithm, QEPS, introduced by Zhang et al. in 2008. This is the first attempt to analyze the dynamic behaviour of membrane algorithms. We use four convergence measures and six population diversity measures to comparatively analyze the evolution processes of QEPS and its counterpart quantum-inspired evolutionary algorithm (QIEA) in an experimental way. Results show that QEPS achieves better balance between convergence and diversity than QIEA, which indicates QEPS has a stronger ability to balance exploration and exploitation than QIEA to avoid premature convergence problem and improve the algorithm performance. This work is very helpful to understand the advantages of the introduction of P systems into evolutionary algorithms.