Local identifiability of a parameter function in a system of differential equations

TL;DR

This paper extends the understanding of local parameter identifiability in differential equation systems, providing new conditions for cases where parameter dimensions are less than or equal to solution dimensions, based on finite observations.

Contribution

It broadens previous results by considering a wider class of systems and cases with differing parameter and solution dimensions, establishing new sufficient conditions for local identifiability.

Findings

Derived sufficient conditions for local identifiability based on finite observations.

Extended previous results to systems with unequal parameter and solution dimensions.

Applicable to a broader class of differential equation systems.

Abstract

In this paper, we consider the problem of local parameter identifiability of a parameter function in a system of ordinary differential equations. Previously, in this problem, the case where the dimensions of a parameter and a solution of a system coincide was considered, and a specific class of systems was identified, for which sufficient conditions for local parametric identifiability were obtained. We extend these results and consider a wider class of systems of differential equations, as well as the case where the dimension of a parameter is less than or equal to the dimension of a solution of a system. In both cases, sufficient conditions are derived for the local identifiability of a parameter function based on observations of a solution at a finite number of points.