Exploiting Variable Sparsity in Computing Equilibria of Biological Dynamical Systems by Triangular Decomposition

Abstract

Biological systems modeled as dynamical systems can be large in the number of variables and sparse in the interrelationship between the variables. In this paper we exploit the variable sparsity of biological dynamical systems in computing their equilibria by using sparse triangular decomposition. The variable sparsity of a biological dynamical system is characterized via the associated graph constructed from the polynomial set in the system. To make use of sparse triangular decomposition which has been proven to maintain the variable sparsity when a perfect elimination ordering of a chordal associated graph is used, we first study the influence of chordal completion on the variable sparsity for a large number of biological dynamical systems. Then for those systems which are both large and sparse, we compare the computational performances of sparse triangular decomposition versus ordinary one with experiments. The experimental results verify the efficiency gains in sparse triangular decomposition exploiting the variable sparsity.