Asymptotic parameter sensitivity for polynomial dynamical systems

Abstract

The effect of parameter perturbations on the trajectories of dynamical systems has been extensively studied in the literature. The effect of parameter values on the number and type of rest-points in a dynamical system has received less attention. For systems that exhibit input multiplicities, the sensitivity of system trajectories to parameter values can be discontinuous when state trajectories are near the boundary between the basins of different attractors. In this work, a computational scheme for conducting a single and joint parameter sensitivity analysis for systems with multiple steady states is presented. The proposed approach is computationally efficient and relies on algebraic geometric tools to obtain a simplified polynomial representation of the system at steady state. The proposed approach is applied to a model of the human hypothalamic-pituitary-adrenal axis and is shown to be relevant to the development of mechanistic models of chronic diseases.