Inverse problem of the Holling-Tanner model and its solution

Q2 Agricultural and Biological Sciences
A. Adeniji, I. Fedotov, M. Shatalov
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引用次数: 2

Abstract

In this paper we undertake to consider the inverse problem of parameter identification of nonlinear system of ordinary differential equations for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval. In this model the equations are nonlinearly dependent on the unknown parameters. By means of the proposed transformation the obtained equations become linearly dependent on new parameters functionally dependent on the original ones. This simplification is achieved by the fact that the new set of parameters becomes dependent and the corresponding constraint between the parameters is nonlinear. If the conventional approach based on introduction of the Lagrange multiplier is used this circumstance will result in a nonlinear system of equations. A novel algorithm of the problem solution is proposed in which only one nonlinear equation instead of the system of six nonlinear equations has to be solved. Differentiation and integration methods of the problem solution are implemented and it is shown that the integration method produces more accurate results and uses less number of points on the given time interval.
Holling-Tanner模型的逆问题及其求解
在本文中,我们致力于考虑非线性常微分方程组参数辨识的反问题,对于有限时间间隔内有限点的Holling-Tanner模型解的完全信息的特定情况。在该模型中,方程非线性地依赖于未知参数。通过所提出的变换,所获得的方程在函数上与新参数线性相关。这种简化是通过以下事实实现的:新的参数集变得依赖,并且参数之间的相应约束是非线性的。如果使用基于拉格朗日乘子引入的传统方法,这种情况将导致非线性方程组。提出了一种新的问题求解算法,该算法只需求解一个非线性方程,而不必求解六个非线性方程组。实现了问题求解的微分和积分方法,结果表明,积分方法在给定的时间间隔内产生了更准确的结果,并且使用了更少的点数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biomath
Biomath Agricultural and Biological Sciences-Agricultural and Biological Sciences (miscellaneous)
CiteScore
2.20
自引率
0.00%
发文量
6
审稿时长
20 weeks
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