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2000 | 27 | 1 | 113-126
Tytuł artykułu

Periodic dynamics in a model of immune system

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to study periodic solutions of Marchuk's model, i.e. the system of ordinary differential equations with time delay describing the immune reactions. The Hopf bifurcation theorem is used to show the existence of a periodic solution for some values of the delay. Periodic dynamics caused by periodic immune reactivity or periodic initial data functions are compared. Autocorrelation functions are used to check the periodicity or quasiperiodicity of behaviour.
Rocznik
Tom
27
Numer
1
Strony
113-126
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-08
Twórcy
autor
  • Institute of Applied Mathematics and Mechanics, Department of Mathematics, Computer Sciences and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • [1] A. Asachenkov, G. I. Marchuk, R. Mohler, and S. Zuev, Disease Dynamics, Birkhäuser, Boston, 1994.
  • [2] L. N. Belykh, Analysis of Mathematical Models in Immunology, Nauka, Moscow, 1988 (in Russian).
  • [3] M. Bodnar and U. Foryś, The model of immune system with time-dependent immune reactivity, preprint Warsaw University, RW 99-04 (52), 1999.
  • [4] M. Bodnar and U. Foryś, The model of immune system with time-dependent immune reactivity, in: Proc. Fourth National Conf. on Application of Mathematics in Biology and Medicine, Warszawa, 1998.
  • [5] M. Bodnar and U. Foryś, Behaviour of solutions of Marchuk's model depending on time delay, Internat. J. Appl. Math. Comput. Sci. 10 (2000), to appear.
  • [6] F. Bofill, R. Quentalia and W. Szlenk, The Marchuk's model in the case of vaccination. Qualitative behaviour and some applications, preprint, Politecnico de Barcelona, 1996.
  • [7] J. Hale, Theory of Functional Differential Equations, Springer, New York, 1977.
  • [8] U. Foryś, Global analysis of Marchuk's model in case of strong immune system, J. Biol. Sys., to appear.
  • [9] U. Foryś, Global analysis of Marchuk's model in a case of weak immune system, Math. Comp. Model. 25 (1995), 97-106.
  • [10] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Acad. Publ., 1992.
  • [11] A. V. Kim and V. G. Pimenov, Numerical Methods for Delay Differential Equations. Application of i-smooth Calculus, notes of lectures at the Seoul National Univ., 1999.
  • [12] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, London, 1993.
  • [13] G. I. Marchuk, Mathematical Models in Immunology, Nauka, Moscow, 1980 (in Russian).
  • [14] G. I. Marchuk, Mathematical Models in Immunology, Optimization Software, New York, 1983.
  • [15] G. I. Marchuk, Mathematical Modelling of Immune Response in Infectious Diseases, Kluwer Acad. Publ., 1997.
  • [16] H. G. Schuster, Deterministic Chaos. An Introduction, VCH Verlagsgesellschaft, Weinheim, 1988.
  • [17] W. Szlenk and C. Vargas, Some remarks on Marchuk's mathematical model of immune system, preprint CINVESTAV Mexico, 1995.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv27i1p113bwm
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