Linear approximation of nonlinear polynomial catenary systems with n compartments

Abstract

Nonlinear polynomial compartmental systems arise in population dynamics and mass transfer modeling. This paper addresses the inverse problem of identifying exchange coefficients from partial measurements of n-1 compartments after injecting a known quantity into the first. We approximate the nonlinear system by a linear one via a Taylor expansion around a reference point, allowing explicit computation of approximate coefficients using the Jacobian. This approach provides a practical framework for parameter identification in nonlinear compartmental systems while leveraging classical linear system techniques.