Special algorithm for stability analysis of multistable biological regulatory systems. (September 2015)

• Record Type: Journal Article
• Authors: Hong, Hoon; Tang, Xiaoxian; Xia, Bican
• Is Part Of: Journal of symbolic computation. Volume 70(2015)
• Page Start: 112
• Page End: 135
• Publication Date: 2015-09
• Subjects: Quantifier elimination -- Root classification -- Biological regulation system -- Stability; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2014.09.039
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier elimination algorithms, in particular real root classification algorithms. However, it is well known that they can handle only very small cases due to the enormous computing time requirements. In this paper, we present a special algorithm which is much more efficient than the general methods. Its efficiency comes from the exploitation of certain interesting structures of the family of differential equations.