一维动力系统的大范围非线性化近似方法及其在一个商品定价模型中的应用

Non-linearized approximation method for one-dimensional dynamical systems with an application to a pricing model of commodity

因为分析含有多个平衡点，或者超越函数的一维动力系统的可积性和稳定性通常是困难的，所以对一维动力系统进行简化是一个很有意义的问题．对含有2-3个平衡点的一维动力系统，根据系统右端函数的7种情况，利用Lagrange和Hermite插值多项式的方法，提出了相应的7类大范围最低次非线性化近似系统，通过积分近似系统得出部分近似解，通过稳定性分析得出平衡点的稳定性保持结果．最后，将一种近似方法应用于一个商品定价模型的具体分析，得到了定价模型的平衡价格的稳定性和动态价格的近似表达式．

Because it is often difficult to analyze the integrability and stability of one- dimensional dynami- cal systems with multiple equilibriums or transcending functions such dynamical systems. According to seven different cases of the , it is a very significant problem for simplifying functions on the right hand of one - dimensional dynamical systems with two or three equilibriums, seven kinds of non - linearized approximate systems are present by using Lagrange and Hermite interpolation polynomials. Approximate solutions are given by integrating the non - linearized approximate systems. It is found that the stability of the equilibriums is preserved by the new approx- imate methods. Finally, one of the non - linearized approximation methods is applied to analyze a pricing model of commodity concretely, for which the stability of equilibriums and the explicit approximate expression of the dy- namical price are obtained.