Title: Asymptotic parameter sensitivity for polynomial dynamical systems

Authors: A. Ben-Zvi, K. Aschbacher

Addresses: Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6H 3P4, Canada. ' Department of Psychiatry, School of Medicine, University of California San Francisco, San Francisco, CA 94143-0848, USA

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.

Keywords: parameter estimation; bi-stability; parameter sensitivity; polynomial dynamical systems; Grobner basis; system trajectories; hypothalamic-pituitary-adrenal axis; mechanistic models; chronic diseases.

DOI: 10.1504/IJAMECHS.2011.040163

International Journal of Advanced Mechatronic Systems, 2011 Vol.3 No.1, pp.54 - 64

Published online: 18 Mar 2015 *

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