Chaos
Feedback | Help | Exit
Chaos
Search:
   
 
 
 
Previous Article
Bifurcation and chaos in spin-valve pillars in a periodic applied magnetic field
We study the bifurcation and chaos scenario of the macromagnetization vector in a homogeneous nanoscale-ferromagnetic thin film of the type used in spin-valve pillars. The underlying dynamics is descr...
Next Article
Synchronization in coupled time-delayed systems with parameter mismatch and noise perturbation
In this paper, a design of coupling and effective sufficient condition for stable complete synchronization and antisynchronization of a class of coupled time-delayed systems with parameter mismatch an...

Chaoticity of the blood cell production system

Chaos 19, 043112 (2009); doi:10.1063/1.3258364

Published 6 November 2009

You are logged in to this journal.

Ryszard Rudnicki
Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland and Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
We present a structured model of stem cells given by a partial differential equation. This equation generates a semiflow acting on the set of densities. We show that this semiflow possesses an invariant exact measure positive on open sets. From this it follows that the system is chaotic, i.e., it has dense trajectories and each trajectory is unstable. ©2009 American Institute of Physics
History: Received 7 July 2009; accepted 14 October 2009; published 6 November 2009
Permalink: http://link.aip.org/link/?CHAOEH/19/043112/1
FULL TEXT OPTIONS   (FREE)
Download PDF (434 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 87.10.Ed
    Differential equations, integrodifferential models (biological/medical physics)
  • 87.10.Mn
    Stochastic modelling (biological/medical physics)
  • 87.19.U-
    Haemodynamics
  • 87.19.rh
    Fluid transport and rheology in tissues and organs (higher organisms)
  • YEAR: 2009

PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (19)
View in Separate Window/Tab
  1. A. Lasota and M. C. Mackey, Chaos, Fractals and Noise. Stochastic Aspects of Dynamics (Springer, New York, 1994), Vol. 97.
  2. D. Ruelle, Turbulence, Strange Attractors, and Chaos (World Scientific, River Edge, NJ, 1995).
  3. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic Theory, Grundlehren der Mathematischen Wissenschaften, Vol. 245 (Springer-Verlag, New York, 1982).
  4. I. D. Chueshov, Introduction to the Theory of Infinite-Dimensional Dissipative Systems (ACTA Scientific, Kharkov, 1999) (translated from the Russian edition).
  5. W. Desch, W. Schappacher, and G. F. Webb, Ergod. Theory Dyn. Syst. 17, 793 (1997).
  6. J. Auslander and J. A. Yorke, Tohoku Math. J. 32, 177 (1980).
  7. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed. (Addison-Wesley, Redwood City, CA, 1989).
  8. L. Glass and M. C. Mackey, From Clocks to Chaos, The Rhythms of Life (Princeton University Press, Princeton, 1988).
  9. A. Lasota, Rend. Semin. Matermatico Univ. di Padova 61, 40 (1979).
  10. P. Brunovský and J. Komornik, J. Math. Anal. Appl. 104, 235 (1984).
  11. R. Rudnicki, Ergod. Theory Dyn. Syst. 8, 437 (1985).
  12. R. Rudnicki, J. Math. Anal. Appl. 133, 14 (1988).
  13. R. Rudnicki, Math. Methods Appl. Sci. 27, 723 (2004). [Inspec]
  14. A. Lasota, Nonlinear Anal. Theory, Methods Appl. 5, 1181 (1981).
  15. P. Brunovský, Nonlinear Anal. Theory, Methods Appl. 7, 167 (1983).
  16. M. C. Mackey and P. Dörmer, Cell Tissue Kinet. 15, 381 (1982). [ISI] [MEDLINE]
  17. A. Lasota, M. C. Mackey, and M. Wazewska-Czyzewska, J. Math. Biol. 13, 149 (1981). [ISI] [MEDLINE]
  18. S. I. Rubinow, Biophys. J. 8, 1055 (1968). [ISI] [MEDLINE]
  19. A. D. Wentzell, A Course in the Theory of Stochastic Processes (Nauka, Moscow, 1975) (in Russian).






Copyright © American Institute of Physics