生态系统的参数确定问题

Determination of the Parameters of the Ecosystem

通过不同观测数据研究捕食者—被捕食者生态系统参数确定问题.研究了四种情形1.观察数据无误差,并已知一个参数值.这种情况下,参数可由其相轨线和最小二乘法精确确定.2.观察数据无误差,但所有参数未知.此时仅靠相轨线的研究,无论给出多少组精确数据,都无法精确确定这些参数.通过原非线性模型的数值计算和网格搜索法,至少需要4组数据,同样得到了精度较高的参数值.3.当观测数据有误差时,根据解的周期性,引入标准周期的概念,在一个标准周期里讨论参数的确定问题,并利用标准周期内的捕食者与被捕食者的数量均值与系统的平衡点的关系对参数进行修正,然后使用网格法进行搜索,进一步提高了参数的精度.4.当观测时间也有误差时,先选取相对最优的随机正态数对观测时刻进行修正,然后再利用3.的方法估计参数.

Based on the different kinds of the observation data about a predators-prey ecosystem, we studied the problem of determining the parameters. There are four different cases in the article. Case 1, when there is no error with the observation data and a parameter is known, then the other parameters can be accurately determined by its orbit and least squares method. Case 2, when there is still no error with the observation data, but no parameter is known, then in this case these parameters can not be accurately determined only by its orbit. However, through the effective grid research of the nonlinear model, at least four sets of data are needed to attain the high precisioon parameters. In case 3, there are errors with the observation data. We introduce a standard cycle, according to the cyclical nature of the solution to the ecosystem. Then we research on the determination of the parameters with the data of this standard cycle. Moreover, with the relation between the mean of predators and preys and the balance of the system, we adjust the parameters using grid research method. In case 4, when there are not only erros with observation data, but also with observation time, we modify the time first with relative optimal normal random numbers, then estimate the parameters with the same method used in case 3.