中文摘要：

目的：研究在等输入模型下 DNA 序列熵随世代变化的规律及其性质。方法：基于 Shannon 信息熵理论，在等输入模型下建立有限长 DNA 序列点突变微分方程组模型，利用 Lagrange 乘数法进行理论证明，并用 Mathematica 软件模拟等输入模型下 DNA 序列熵的变化过程。结果：DNA 序列在等输入模型下发生突变，其熵随世代增加随机波动，且趋于最大值。结论：DNA 序列点突变具有“保熵性”，并验证了生物是朝着多样性增大方向进化的理论。

英文摘要：

Aim：To further understanding the foundation of the mechanism of biological evolution,the changing of the entropy of DNA sequences among the generations was characterized using the equal-input model,which is a more complicated substitution model.Methods：Based on Shannon entropy theory,a set of differential equations was founded about point mutations of DNA sequence with limited length in the equalinput model,the theoretical demonstration was proved by the Lagrange multiplier method,and Mathematica was used to simulate the changing of the entropy of DNA sequences.Results：The mutations in the DNA sequences occurred in the equalinput model,the entropy fluctuated as the generations,and tended to be maximum.Conclusion：The point mutations in the DNA sequences can maintain their entropy,and it was verified that biodiversity of species increased during evolvement.