小麦蜡熟期茎杆抗倒伏数学模型的建立  

Mathematical Model of the Wheat Stem Lodging at Dough Stage

作　　者：钱兵[1] 张海龙[2] 李静波[2] 

机构地区：[1]南京师范大学社会发展学院,江苏南京210097 [2]南京师范大学电气与自动化工程学院,江苏南京210097

出　　处：《数学的实践与认识》2012年第15期20-35,共16页Mathematics in Practice and Theory

摘　　要：以物理学力学理论为基础,在考虑小麦穗自重,风力大小、风力大小、方向及作用点的因素下,将茎杆状态分为无风情况下的静态过程和有风情况下的动态过程,分别建立小麦蜡熟期茎杆的静态和动态抗倒伏模型.提出合理假设,得到2008年和2011年数据中各品种的机械强度、茎杆鲜重和重心高度的计算公式,再结合已给的倒伏指数公式,计算得到各小麦品种的倒伏指数;接下来,通过斯皮尔曼相关系数分判断倒伏指数与外部特征因素的相关性大小;最后,在考虑穗自重,风力大小、方向及作用点,茎杆变形能的影响因素下,分别建立小麦抗倒伏静态模型和动态模型.其中静态模型以临界力为计算目标,动态模型同时考虑穗自重和风载因素,最终将静态模型和动态模型结合作为小麦抗倒伏模型.文章最后利用已知数据,计算得到抗倒伏模型各个参数,同时对动态模型进行仿真,得到在一定风速下茎杆摆动的运动轨迹.在此基础上,考虑到该模型为典型的非线性动力模型,利用相平面分析法发现存在明显混沌现象,并进一步找出可能导致混沌的相关特性参数.Consider the Spike weight, size, direction and point of action of the wind factor based on physics mechanics, stem state is divided into a dynamic process in the case of the wind and a static process in the case of no wind, namely the establishment of wheat the dough of the stem of the static and dynamic lodging model. The mechanical strength of the data of all varieties in 2008 and 2011, stem fresh weight and center of gravity formula, combined with lodging index formula has to be calculated lodging index of all wheat varieties on Reasonable assumptions; and through the Spearman correlation coefficient to determine correlation of the lodging index and factors of the size of the external characteristics; Finally, consider the factors affecting ear weight, wind speed, direction and point of stem deformation energy, respectively, to establish the static model and dynamic model of wheat lodging. Static model to the critical force, the dynamic model taking into account the spike weight and wind are set out factors, and ultimately combined with the static and dynamic models as the wheat lodging model. In the end of paper, using the known data to calculate the lodging model parameters, while the dynamic model to simulate wind stems swing trajectory. On this basis, taking into account the model for a typical nonlinear dynamic model, the phase plane analysis found that there is obviously chaotic phenomena, and identify areas that may lead to chaos parameters.

关 键 词：小麦抗倒伏 倒伏指数 抗倒伏模型 混沌现象 

分 类 号：O242.1[理学—计算数学]