Identifiability in networks of nonlinear dynamical systems with linear and/or nonlinear couplings

Abstract

The identifiability study of dynamical systems is a property that ensures the uniqueness of parameters with respect to the model’s measurement(s). Several methods exist, but for nonlinear differential equations, these methods are often limited by the size of the systems. Some recent work on network identifiability has been published, but strong constraints on the system’s linearities and coupling functions are still imposed. Unfortunately, in fields like neuroscience, such restrictions are no longer applicable due to the complex dynamics of the neurons and their interactions. This paper aims to present a method for studying identifiability in networks composed of linear and/or nonlinear systems with linear and/or nonlinear coupling functions. Based on the observation of certain variables of interest of some nodes, it determines which subsystems are identifiable. Additionally, the method outlines the paths and steps required to identify these subsystems. It has been automated by an algorithm described in this paper, implemented in Maple and applied to an example in neuroscience, a neural network of the C. elegans worm.