Inverse Problems of the Holling-Tanner Model Identification with Incomplete Information

Abstract

In this paper we present a novel method for numerical parameter identification of the Holling-Tanner model with incomplete information. It means that information about predator or prey is unavailable, or only particular information about these species is available. The proposed method is based on elimination of variable characterizing unknown population from the original system of equations and obtaining a new nonlinear ordinary differential equation. In this equation, the dependent variable characterizes dynamics of the known population and new set of parameters functionally depends on the original unknown parameters. In the case of the Holling-Tanner model, the number of new parameters is higher than the number of original unknown parameters. Hence, there exist several constraints between new unknown parameters, which must be taken into consideration in the process of the parameter identification. The conventional method, based on the Lagrange constraint minimization of a goal function gives a nonlinear system of equations where the number of equations is equal to the sum of new unknown parameters and constraints. In this novel method, proposed in this paper, the number of equation is exactly equal to the number of constraints which substantially simplifies solution of the problem.