【摘要】 研究了捕食者模型在多种观测值条件下的非线性微分方程组参数拟合问题.首先利用龙格-库塔法进行微分方程数值计算,通过首次积分项变形建立线性回归方程,进行最小二乘拟合;其次,考虑到实验数据包含随机误差的扰动,引进正规方程组对模型进行误差分析;最后针对时间变量也出现误差,采用拉依达准则筛选,然后提出了一种较为简单的参数分段动态估计算法.更多还原

【Abstract】 The problem of parameters fitting for nonlinear differential equations in the Predator-Prey model is studied.Firstly,the Runge-Kutta method is used to carry on numerical calculation and linear regression equations through the transmutation of the first integral parts are constructed,then fits them using least-squares method;Secondly,considering the distribution of random error in the experimental data,this paper introduces the normal equations to analyze the model;Finally,aiming at the conditions that the time variables also include error,this paper uses 3σ law to filter the data and then presents a simple method of dynamic parameter subsection estimation.更多还原