中文摘要：

本文提出了一个3种类聚集体问基于催化复制的耦合模型，通过该模型近似模拟DNA分子链在RNA催化酶的催化下的复制和聚合过程。在平均场理论下，利用反应速率方程方法研究了系统的动力学演化行为，获得了DNA分子链的集团总数量、集团总质量以及浓度分布随时间的具体演化规律的解析解。结果表明：DNA分子链集团的总数量N（f）在长时间下会达到一个与其初始值无关的常数；集团总质量M（f）随时间呈指数性增加；浓度分布ak（f）在长时间下也趋于常数，即系统最终会达到平衡态。

英文摘要：

We propose an aggregation model with catalyzed-duplication process of three species to mimic the coagulation and duplication of DNA helix with the help of catalytic RNA. By employing the mean-field rate equation approach we analytically investigate the evolu- tion behavior of the system. The kinetics of the total number,the total mass and the aggregation size distribution of the DNA polymer system are derived. The result implies,the total number of the DNA polymers N（t） can approach a constant value which is independent with the initial value in the long time limit, the total mass M（t） increases with time exponentially,and the aggregate size distribution ak （t） may approach a constant value,that is,the system will eventually evolves into a steady state.