Periodic dynamics in a model of immune system

Volume 27 / 2000

Marek Bodnar, Urszula Foryś Applicationes Mathematicae 27 (2000), 113-126 DOI: 10.4064/am-27-1-113-126


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.


  • Marek Bodnar
  • Urszula Foryś

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