期刊
AIMS MATHEMATICS
卷 6, 期 7, 页码 6781-6814出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2021398
关键词
singular perturbation; slow manifold; quasi-steady state; Michaelis-Menten mechanism; critical manifold; Gronwall lemma; Poincare sphere
资金
- University of Michigan Postdoctoral Pediatric Endocrinology and Diabetes Training Program Developmental Origins of Metabolic Disorder (NIH/NIDDK) [K12 DK071212]
- Natural Sciences and Engineering Research Council of Canada
- bilateral project [ANR-17-CE40-0036, DFG-391322026]
The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis-Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. Distinguished invariant manifolds and time scale estimates were obtained for both settings, with a highlight on the special role of singular perturbation parameters in higher order approximations of slow manifolds. The paper concludes with a discussion of distinguished invariant manifolds in the global phase portrait.
The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis-Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait.
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