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.
Highlights
The numerical evaluation of known coefficient of a dynamical system i.e. the problem of dynamical system identification, is one of the most important problem of the mathematical biology [1], ecology [2], [3], [4], etc
In the present paper we consider the inverse problem of parameter identification of the Holling-Tanner predator-prey model [5], [6]. This model is widely used in mathematical biology, for example, in the study of transmissible disease [7]
The main disadvantage of the conventional method of constraint minimization by means of the Lagrange multipliers is that the method generates a system of six nonlinear equations with unknown initial guess values
Summary
The numerical evaluation of known coefficient of a dynamical system i.e. the problem of dynamical system identification, is one of the most important problem of the mathematical biology [1], ecology [2], [3], [4], etc. In the present paper we consider the inverse problem of parameter identification of the Holling-Tanner predator-prey model [5], [6]. This model is widely used in mathematical biology, for example, in the study of transmissible disease [7]. M.Y. Shatalov, Inverse problem of the Holling-Tanner model and its solution is complete statistical information about the unknown function. The problem of the Holling-Tanner model identification has its specifics, because it nonlinearly depends on the unknown parameters. It is possible to transform this model to a new form where the equations of the system linearly depends on the set of new parameters These new parameters are not independent and we need to consider the constraint between the parameters, which are nonlinear. It is shown that the integration methods is more accurate than the differentiation one and needs less amount of experimental information
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