A robust Lyapunov criterion for nonoscillatory behaviors in biological interaction networks
File(s)
Accepted version
Author(s)
Angeli, David
Al-Radhawi, Muhammad Ali
Sontag, Eduardo D
Type
Journal Article
Abstract
We introduce the notion of nonoscillation, propose a constructive method for its robust verification, and study its application to biological interaction networks (also known as, chemical reaction networks). We begin by revisiting Muldowney’s result on the nonexistence of periodic solutions based on the study of the variational system of the second additive compound of the Jacobian of a nonlinear system. We show that exponential stability of the latter rules out limit cycles, quasi-periodic solutions, and broad classes of oscillatory behavior. We focus then on nonlinear equations arising in biological interaction networks with general kinetics, and we show that the dynamics of the aforementioned variational system can be embedded in a linear differential inclusion. We then propose algorithms for constructing piecewise linear Lyapunov functions to certify global robust nonoscillatory behavior. Finally, we apply our techniques to study several regulated enzymatic cycles, where available methods are not able to provide any information about their qualitative global behavior.
Date Issued
2022-07-01
Date Acceptance
2021-07-03
Citation
IEEE Transactions on Automatic Control, 2022, 67 (7), pp.3305-3320
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
3305
End Page
3320
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
67
Issue
7
Copyright Statement
Copyright © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000818858700009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Kinetic theory
Substrates
Regulation
Compounds
Additives
Oscillators
Biological interactions
Biological interaction networks (BINs)
enzymatic cycles
piecewise linear (PWL) Lyapunov functions
robust nonoscillation
second additive compounds
GLOBAL ASYMPTOTIC STABILITY
CHEMICAL-REACTION NETWORKS
STRUCTURAL STABILITY
SYSTEMS
INJECTIVITY
MODEL
Publication Status
Published
Date Publish Online
2021-07-14