中文摘要：

有限生物模型是对实际生物现象进行模拟的有效数学模型，模型的平衡点及其个数对于定性研究实际生物系统的动力学特征有着重要意义。首次系统化地利用三角列这一计算机代数工具对此类模型的平衡点及其个数问题进行研究，并阐明了三角列方法在这一问题上结构清晰、参数处理方式简单等优点。在几个实际生物模型上的应用验证了三角列方法的有效性。

英文摘要：

The finite biological model is an effective mathematical model for simulating the practical biological phenomena, and the steady states and their numbers are important in the qualitative analysis of dynamic characteristics of practical biological models. This paper makes use of triangular sets, a tool from computer algebra, to systematically study the steady states and their numbers for such models for the first time, and demonstrates the advantages of the application of triangular set methods on this problem, such as clear structure and convenient parameter handling etc. The effectiveness of the triangular set method is verified by the application to several practical biological models.