Local bifurcations of an enzyme-catalyzed reaction system with cubic rate law

Local bifurcations of an enzyme-catalyzed reaction system with cubic rate law In this paper, we study the dynamics of a system arising from enzyme-catalyzed reaction. Parameter conditions for the existence and qualitative properties of equilibria are given. Various kinds of bifurcations including saddle-node bifurcation, Bogdanov–Takens bifurcation and Hopf bifurcation are investigated. The order of weak focus is proved to be at most 2, and the parameter conditions of exact order are obtained. Numerical simulations are employed to illustrate the results obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Local bifurcations of an enzyme-catalyzed reaction system with cubic rate law

Local bifurcations of an enzyme-catalyzed reaction system with cubic rate law

Nonlinear Dyn (2018) 94:521–539 https://doi.org/10.1007/s11071-018-4375-y ORIGINAL PAPER Local bifurcations of an enzyme-catalyzed reaction system with cubic rate law Juan Su · Bing Xu Received: 17 December 2017 / Accepted: 17 May 2018 / Published online: 31 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract In this paper, we study the dynamics of reaction scheme is given in Fig. 1. The change of reac- a system arising from enzyme-catalyzed reaction. tants in this scheme can be described by the following Parameter conditions for the existence and qualita- system (see [5,21]) tive properties of equilibria are given. Various kinds of s˙ = α − V (s, p) − V (s), 1 3 bifurcations including saddle-node bifurcation, (1.1) p ˙ = β(V (s, p) − V (p)), 1 2 Bogdanov–Takens bifurcation and Hopf bifurcation are where s, p ≥ 0 denotes the concentrations of substrate investigated. The order of weak focus is proved to be at most 2, and the parameter conditions of exact order S and product P, respectively, V is the rate law func- tion of S converting into P such that V (0, p) = 0, are obtained. Numerical simulations are employed to illustrate the results obtained. ∂V /∂s > 0 and ∂V /∂p > 0for s > 0 and p > 0, 1 1 V (p) ≥ 0 and V (s) ≥ 0 represent the sink rate func- 2 3 Keywords Enzyme-catalyzed reaction · Saddle-node tions of P and S respectively, and α, β> 0 are kinetics constants. Moreover, system (1.1) with V (s) ≡ 0 cor- bifurcation · Bogdanov–Takens bifurcation · Hopf bifurcation · Resultant responds to the removal of branched sink of S in Fig. 1, and has been discussed extensively in [6,10,11,18,19] and the references therein. Mathematics Subject Classification 34C23 · 92C45 System (1.1) with V (s) ≡ 0 includes several spe- cial cases studied in previous works. 1 Introduction...
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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-018-4375-y
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the dynamics of a system arising from enzyme-catalyzed reaction. Parameter conditions for the existence and qualitative properties of equilibria are given. Various kinds of bifurcations including saddle-node bifurcation, Bogdanov–Takens bifurcation and Hopf bifurcation are investigated. The order of weak focus is proved to be at most 2, and the parameter conditions of exact order are obtained. Numerical simulations are employed to illustrate the results obtained.

Journal

Nonlinear DynamicsSpringer Journals

Published: May 31, 2018

References

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