Bifurcation of nontrivial periodic solutions for a biochemical model with impulsive perturbations
type: Item
instance of: scholarly article
title: Bifurcation of nontrivial periodic solutions for a biochemical model with impulsive perturbations
zbMATH Open document ID: 1183.34066
author: Zhong Zhao
author: Li Yang
author: Lansun Chen
published in: Applied Mathematics and Computation
publication date: 2010-01-08T00:00:00Z
review text: The authors consider a basic biochemical reaction of the form (1.1): \[ \begin{aligned} \dot x(t) & = a-(kx(t)- bx(t)y(t),\\ \dot y(t) & = bx(t)y(t)- {qy(t)\over c+q(t)},\end{aligned}\qquad t\neq nT \] \[ \begin{aligned} \Delta x(t) & = p,\\ \Delta y(t) & = 0,\end{aligned}\qquad t= nT \] there are \(x(t)\) and \(y(t)\) the concentrations of the two internal reactants \(\Delta x(t)= x(t^+)- x(t)\), \(\Delta y(t)= y(t^+)- y(t)\), \(n= \{1,2,3,\dots\}\), \(P> 0\), \(T\) is the impulse period, the function \({q\over c+y}\) is the saturation of the input. By using Floquet theorem the authors find a number \(T^*\) so that the boundary-periodic solution \((\widetilde x(t),0)\) of (1.1) is locally stable if \(T^*< T\) and is unstable if \(T< T^*\).
reviewed by: S. Kostadinov
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 5655268
zbMATH Keywords: impulse perturbation
zbMATH Keywords: Floquet theorem
zbMATH Keywords: asymptotical stability
MaRDI profile type: Publication
full work available at URL: j.amc.2009.06.070
OpenAlex ID: W2012884516
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DOI: 10.1016/J.AMC.2009.06.070
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description: scientific article; zbMATH DE number 5655268