Translator Disclaimer
July/August 2009 A sharp condition for the chaotic behaviour of a size structured cell population
S. EL Mourchid, A. Rhandi, H. Vogt, J. Voigt
Differential Integral Equations 22(7/8): 797-800 (July/August 2009).

Abstract

We show that the condition $0\le \beta \le \frac{1}{2\ln 2}$ is necessary for the chaoticity of the solution of the cell population model \begin{equation}\label{eq1} \left\{\begin{array}{ll} \frac{\partial u(t,x)}{\partial t}=-\frac{\partial(x u(t,x))}{\partial x}+\gamma u(t,x)-\beta u(t,x)+4\beta u(t,2x)\chi_{(0,\frac{1}{2})}(x),\\ u(0,\cdot)= f \in L^1(0,1). \end{array} \right. \end{equation} (If $\gamma -3\beta >0$, then this condition is known to be sufficient.) The analysis depends on solving a forward delay equation.

Citation

Download Citation

S. EL Mourchid. A. Rhandi. H. Vogt. J. Voigt. "A sharp condition for the chaotic behaviour of a size structured cell population." Differential Integral Equations 22 (7/8) 797 - 800, July/August 2009.

Information

Published: July/August 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.37088
MathSciNet: MR2532122

Subjects:
Primary: 37N25
Secondary: 35F10, 37D45, 92D25

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
4 PAGES


SHARE
Vol.22 • No. 7/8 • July/August 2009
Back to Top